On small boards, like 9x9, area counting is often quite easy, if the board is (nearly) split in half. You just need to count along the diagonal or central line, and account for any stones over the line.
Black controls 5 points along the diagonal, while White only has 4. They each have one stone past the line, so those cancel out. Black+1
White controls 5 points along the middle line, while Black only has 4. They each have three stones past the line, so those cancel out. White+1.
White only controls 4 points along the middle line, compared to Black’s 5. However, White has a one stone advantage (3 vs 2) beyond the center line, which is worth a two-point swing (+1 area for White, while -1 for Black). Hence, this last example is White+1 overall.
These are all one-point games, and it’s even more obvious by examining the center line when the margin is larger.
If both players have played an equal number of stones (and there are no tricky situations, like seki), the area count is equal to the territory count. This will be the case if both players have passed an equal number of times and White played the last stone. If Black played last, then that typically (unless that last stone is dead, or something more convoluted and rare happens) makes Black’s score one point larger under area scoring than under territory scoring.