Chinese checkers stones can jump.
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Chinese checkers is played with pegs, pieces, or marbles. I couldn’t find an example of chinese checkers stones… same with draughts (checkers).
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Chinese checkers marbles are made of glass, and as you know, some go “stones” are made of glass, but are called “stones” nonetheless.
Edit: Indeed, glass is made of silica, a mineral constituent that takes the forms of sand and quartz. Glass is also listed in the Dictionary of Geological Terms (AGI, 1957). Consequently, the use of “stone” is entirely appropriate.
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I was going to provide an example of checkers pawns made of marble but then I got caught in a loop from pawns to marble then marbles then pegs then…
Why… why do you call glass spheres “marbles”???
What would you call marble cubes? Bananas??? 
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Jump, skip…are more or less the same no?
Also…
And now I recall Dad teaching me to skim stones when I was a kid. I’d forgotten that!
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I wanted to leave the draughts (checkers) answer to Lys. Now that he has posted, I will add that I have seen a hand-crafted checkers set using black hematite and possibly gypsum (not sure what the white was) at a display of lapidary crafts at my rock club many years ago. Lapidary enthusiasts make all kind of stuff out of stone.
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Positionally, stones can jump. In a sense of capture like with other abstract games, not so much 
Monkey Jump
Reverse Monkey Jump
Small Monkey Jump
One Point Jump
Two Point Jump
Diagonal Jump
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I think both the words “stones” and “jump” are used metaphorically in discussions about Go and other games. Strictly speaking, none of the playing pieces in various board games actually physically jump themselves. Instead, a player may pick them up and moves them to a new spot, maybe while passing over another piece. So, even in a game like checkers, the word “jump” is used in a metaphorical sense. Of course, I think this metaphor is natural since the actual motion of the playing piece is like that of it jumping over another.
In Go, the stones don’t move after they have been placed (except to be removed when captured), but frequently discussions about Go involve metaphors about the “movement” of the stones, and even the word “jump” is widely used in various Go terms, like One-point jump at Sensei's Library, Monkey Jump at Sensei's Library, Two-point jump at Sensei's Library, Diagonal jump at Sensei's Library, etc. Although the individual stones are not being moved after they have been placed, the metaphor still seems natural when one views groups of stones as a collective whole, with the concept of “jumping” relating to how the group changes and expands it area of influence.
While a lot of these abstract board games could be played with game pieces that consist of actual stones, quite often, however, the game pieces are not actually made of stone, nor necessarily in some sort of shape that would resemble a natural, found stone. Go “stones” is metaphorically understood to refer to the playing pieces used for Go, regardless of their material(s), provided they suit the purpose. I think that one could extend this analogy to call the playing pieces of other games as “stones” as well, however that might not be commonly done, except for some games like mancala or curling. Some other games might even use manufactured playing pieces made of stone, even if the users might not call them as such.
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Returning to chinese checkers, I don’t think that what the pieces are made of is relevant. You can have plastic pegs and stone marbles but they are still called pegs and marbles.
I’d be interested to see a reference where chinese checkers pieces are called stones. That would sure shut me up 
I’m not a research service, and I am not trying to shut you up. This began as a discussion about jumping stones. Now I see the ground has shifted to semantics/linguistics.
As a kid, through elementary school, we played a lot of marble games, Chinese checkers, and mancala (as I have talked about in other threads). The stones in mancala, by the way, also jump—from bowl to bowl. (I acknowledge that quotidian people may call it “moving,” but getting out of a bowl actually requires jumping, albeit with the help of a human hand.) We usually played with a commercial set at a quasi-rec center, but one kid had a collection of light and dark stones (dark gray gravel that was widely abundant), so the game could be played anywhere by digging some shallow holes in the dirt. Under the influence of mancala, I think, we tended to mix our terms in CC, between “marble” and “stone,” but I can’t rightly say which was dominant. Even “piece” was used occasionally.
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That’s why it’s in the Pedantry thread, where the denizens enjoy sententious banter 
I’m totally with you on this one. Checker’s stone definitely jump. No-one said that jump had to mean unassisted self-propelled jump.
You said so! 
more easy tsumego:
https://www.youtube.com/watch?v=r85Fl5UZq18&t=563s
Bear finally gets the ring and goes to the swimming pool
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Wouldn’t that anger you, to be attacked by your enemies?
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No. One expects to be attacked by enemies. What is more dangerous and triggering is to be attacked by “friends.”
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As a first step why do we call chinese checkers, chinese checkers?
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In the United States, the commercialization of Halma (invented c. 1880) occurred in the early 20th century. That coincided with a period of national fascination with the exotic side of Asia, particularly China (despite the so-called “Yellow Peril” propaganda in the first two decades of the 20th century). Consequently, associating the game with China was nothing but a sales gimmick, and “Chinese” checkers was born. I once saw an early Chinese checkers board in an antique shop. It was called “Hop Ching Checkers.” Especially interesting was that the board had 5 rows in the home triangles, rather than the modern 4 rows. I would have bought it, but it was very expensive.
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Looking back, it appears that no one ever answered @Lys’s question about why glass marbles are called “marbles.” The answer is that early marbles (aggies) were typically made of agate, a decorative stone of great variety and popularity in the lapidary field. People might well confuse some agate with marble, or perhaps marble was also used at that time (I don’t know). Glass marbles were a later development, in my day, and were considered an abomination by my parent’s generation. Aggies were still around and prized when I was a kid, and I had a few of them, including several “shooters.” Not sure where my collection is now. I think I passed it on to my “little brother” when I became a teen.
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This meme confused me as we usually oppose big moves vs urgent moves to point that urgent comes before big.
But maybe that is that was intended?