When I googled the word schottische, many definitions came up claiming that the schottische is a kind of polka. I don't see that.

A scottische goes one two three hop, one two three hop, one hop, two hop, three hop, four hop. A polka is far simpler. So how do they figure?

Nobody mentions that while the feet do the above, the body is doing bigger motions - such as turning around, going in and out of the circle, dancing side by side with one's partner, changing partners, etc. There are many versions of these, and thus there are many schottisches.