Snooker uses nap cloth. It's like a dogs fur, basically. The fur will point towards the black spot, so playing from baulk to the black is with the nap. Playing against the nap makes the cueball swerve in the opposite direction of the sidespin. With the nap, it will swerve in the same direction as the sidespin. A ball played along the end rail by the black spot will hug the rail more, while one played along the end rail by the yellow spot will tend to drift out from the rail. These are real effects and sometimes come up when escaping from snookers, trying to pot certain balls etc. If you are barely tapping a ball in from long distance, you may have to account for playing diagonally across the nap. Snooker players, especially those playing on club tables with longer nap than used on tv, DO NOT like to bunt balls in from long distance. The cloth used on tv tables is shorn very thin and does not last long, but also does not have as extreme of a nap effect.
Most modern pool cloths are napless but there are still very, very minute effects like on a nap table. You will generally always have the cueball curve in the direction of the spin, no matter which direction you are playing on napless cloth.
Usually, if you play a 3 railer at slow speed you'll find that a table will have a "long" and a "short" side. A 3 railer started at one end of the table may come shorter than one started at the opposite end.
Depending on manufacturer there might also be a very, very slight curve in the opposite direction playing against the "nap" at the very end of travel, we're talking about the last couple of rotations maybe 1/8 - 1/4 of a balls worth. It's a bit inconsistent and for some cloths may not exist at all. I can't ever remember having this come up and change the outcome of a game on Simonis cloth. I haven't even been able to repeatably demonstrate it on Simonis (760/860) and it may not even exist on that cloth, but it does on some others. There are too many confounding variables on used cloth. The table could be slightly out of level, there could be chalk dust or divots..Generally, it will not come up at all, even if it did it would have near zero impact and could safely be ignored.