All metal is cast. All cymbals are made from metal sheets, except for Ufip rotocast cymbals.
Sheet metal is simply metal formed into thin and flat pieces. It can be formed by stamping, rolling, drawing, ironing, incremental sheet forming and so on.
Common Zildjian-influenced cymbal terminology denotes cast cymbals as cymbals made from sheets made from smaller individual casts, while sheet cymbals are made from pieces cut out from larger sheets, but this is not the core difference. As is explained at the Paiste site, all that really matters is the type of alloy and the annealing, shaping/hammering and lathing process.
So, again, all cymbals are cast, the majority of cymbals is sheet metal and a lot of "pro" cymbals come from larger sheets of bronze.
And buying used is still a great idea.