The distinction between a cutter and a slider is extremely faint; there is no clear line defining when it is one or the other, and not a lot of pitchers actually throw both regularly. So I think saying that definitively one is one thing and one is the other is hazy. I would tend to call a cutter a fastball and a slider a breaking ball, but the cutter to a great extent is a little bit of both. To say that the delivery of one is altered and the other is not seems silly.