@RedAgent14 brought to my attention that I use the terms Moyo and Influence almost interchangeably. I looked up both on Sensei’s and Moyo I understand. But Influence is a bit harder to wrap my head around. Especially as it pertains to the 9x9, where I spend all my time and teach others about the concept of Moyo. In the interest of expanding my own knowledge and better relaying these topics to students in the future, can somebody please explain to me how Influence works on the 9x9, as opposed to Moyo?
There is no moyos nor influence on 9x9, at best you can have loose territories or potential, but trying to create something that even resembles moyo is a losing strategy on 9x9.
Play your first stone as black to 5-5, 5-4 or 4-4 point, that way you have influence and whites first move has to be an invasion of some sort. I think thats the closest you can have “influence” on 9x9 board.
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Interesting that you teach moyos on 9x9,
anyway, moyo can probably also be seen as a “sphere of influence” i.e.: an area that’s not quite territory (because it’s invadable) that you are threatening to make a lot of territory, accompanied by a lot of local stones to fight with.
Influence, on the other hand, is really just a vague term for the idea that “stones nearby make fighting easier”. Now, a moyo does make use of influence, usually coming from the stones threatening to surround, but even if you poke a rod at your opponents moyo, that is a source of “influence” that you can use to invade.
As for application on the 9x9 board, I’m not quite sure.
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[...] On a 19x19 board, influence-oriented play, in which we aim to create a large framework, is rather easier; in the small space of that 9x9 board, however, White can invade Black’s moyo and take away many of those potential points.
I recommend that you play only for control until you have a good, basic understanding of how influence works on the 9x9 board. But what does playing for control mean? It means that the main focus is getting territory. Of course, playing only for territory would be too passive: instead, we must find moves that make solid territory but also create as much influence as possible—and this, by the way, is the very reason why tengen is the most popular opening: it acts as an outpost in the center of the board, allowing us to make territory into any direction.
Remember: control is the main goal on 9x9. Influence is very subtle and not as important for the advanced beginner. Once you have a better grasp of the overall play, you can go back and experiment with influence strategies.
— Immanuel deVillers, 81 Little Lions
(Upcoming 2nd Edition)
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I you define moyo as a framework for potential territory, that is something you kind of see in 9x9 Go. In the game below (ongoing), my opponent made something resembling a moyo, and I played something resembling an invasion.
I’m not sure I would describe this as a moyo, however. A moyo on a 19x19 board envisions a large framework bounded on both sides with some distance between stones. On 9x9, the best you can do is draw your line in the sand, and then call your side a moyo. I’d prefer describing it as Immanuel did above in terms of control.
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I erroneously created a Demo board that I believed was describing the concept of Moyo. I’ve been giving this to my students to try and help them understand how stone placement can affect the game moving forward. Can anyone take a look at this and tell me if what I have here and what I should be calling this, if not Moyo? Is this Control perhaps?
I am unable to understand at what point your opponent had played a Moyo and at what point you played something resembling an invasion. Could you point a specific turn or series of turns? This game has been fascinating to watch by the way 
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One of these days you should consider taking one of your 9x9 games and, turn by turn, providing commentary on your logic and rationalization behind each move. This level of play is beyond my ability to rationalize 
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I guess I need to do some research on Control then. I haven’t spent much time studying Go yet 
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He’s playing off my suggested definition of “moyo” as the same as “sphere of influence”. Within this framework, b builds a “moyo” for the upper side up to move 19 where an invasion is then attempted by move 20. (although I’d argue this invasion shouldn’t work, since at Move 41 b can instead play A8 followed by w A6, b A8, w A7 b E9 and w cannot live)
And he is right that a “moyo” generally refers to large frameworks spanning sections of the board (like the ones which become prominent in sanrensei and Chinese “omoyo” openings).
I’d argue that this has a slight bearing on both topics in a way, but the influence of a stone is more far reaching than just one space (even diagonally), although it does diminish the further out you go (as the further it is, the harder it is to be incorporated into a fight).
One thing to note is that C7 and E7 make solid territory stretching all the way to the edge of the board, making 8 or 9 points (posted a little “minimum points” variation in the comments – but don’t get me wrong, w should definitely not fall back to F8 and instead cut at F6, meaning it’s probably a bit more). Really any two stones 2 spaces or less apart on the third line make territory in more or less the same way (unless b has enough local influence to sweep that out from under).
Meanwhile b up to move 6 has a big moyo (and I think even Mark – I have no idea why I originally wrote adam – here will agree with me that this is a moyo) that extends all the way to his edge of the board. It’s likely invadeable (haven’t checked tho), and b would just love to make it all solid territory given the chance.
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My general understanding of those terms is:
Moyo: an area on the board that is partially surrounded and easy to enclose, that could therefore become territory if the opponent doesn’t take some countermeasure.
Influence: being strong toward an open area. Eg. having a big wall facing the center of the board.
I’ve heard many times from different sources that influence is for fighting, not for territory.
Territory can come as a byproduct of fighting (capturing stones or becoming even stronger toward the other side).
So, on the 9x9 you can’t really have a Moyo.
You can have influence if your opponent makes the mistake of creating a weak group: then, attacking that group you can become stronger on the outside.
Françisa in “81 little lions” uses the example of the 3-3 invasion: on a 9x9 board you can do it, but you lose the rest of the board.
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So, I see a lot of this sentiment, and it seems to kinda be backed up by play, but it’s not that you can’t make a large area that’s partially surrounded and easy to make territory, or make a “sphere of influence”, but rather that doing so is generally considered to be a bad idea on the 9x9 board.
The reason being is that the main strength of a moyo is that if you’re invaded you can either:
A) make enough territory from having the invasion live small,
or
B) gain influence from fighting the invading group so that you can make equal or greater points than the invasion’s value elsewhere.
Typically you can’t get A because it takes quite a few moves to make a moyo, and the opponent will more than likely have enough territory that just living inside your moyo or reducing it (poking it from the outside to make it smaller) will be enough to win.
B is even less likely as the board is so small that by the time you get invaded most of the territories are likely already settled, and you’re not gonna be able to turn the influence you got into a big enough territorial advantage.
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Thank you, every single one of you, for helping me to understand this better. I now understand that Moyo and Influence are not the right terms. It seems like Control is a better fit, but not perfect. I headed over to Sensei’s and I couldn’t find anything on the term Control. Would this concept go by another name? A Japanese, Chinese, or Korean term, perhaps?
Well, it depends on what you mean with “large area”. 
When I think of a moyo on a 19x19 board I imagine something like 40, 50 points. Not already surrounded, so the opponent can do some reduction and bring them to a safe amount.
But how could you “partially surround” more than 15 points on a 9x9 board? Usually the first 4 moves (2 by black and 2 by white) already slice the board in smaller pieces.There’s no room to make a moyo.
Maybe when you play on the 9x9 board with 4 handicap stones, you can call that a moyo! 
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well, I’m more thinking in terms of portion of the board than direct point count, but yeah, if you go by direct point count you’re not gonna get a big moyo
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If you think about it in proportions, a 50 point moyo on a 19x19 board is equivalent to an 11 point moyo on a 9x9 board.
well, of course it’s hard to find one of those (unless you go by my “sphere of influence”, where the invadeable 4-4 serves as a sort of 10 point “moyo”), but I’d argue the comment I made above about the demo board’s framework containing black stones E5, E3, and C7 was a moyo worth ~25 points at best, even by most common definitions – even if it is unlikely to make and probably not amazing even if you do make it.