I like the phrasing used by https://houseofgraphs.org/ — while there are an infinite number of mathematical objects in any category, there are only "a few thousand that can be considered really interesting."
The same with chess and go. There are way too many move order combinations, but only a few thousand interesting ones.
Happy to have authored A094777, Number of legal positions in Go played on an n X n grid (each group must have at least one liberty), [1] and A269417, Number of Go games on n X n board with no repeating position and suicide allowed. [2].