The words get used loosely, so here's what they actually mean.
Sheet vinyl is a PVC-based product supplied on a roll, usually in 2m, 3m or 4m widths. Most modern "lino" is really sheet vinyl.
Cushioned vinyl has a foam layer built in, which makes it softer underfoot and slightly quieter. It's the most common domestic choice.
Linoleum, properly speaking, is a different material altogether: linseed oil, wood flour, resin and jute backing. It's a natural product, it's very hard-wearing, and it's more often specified in commercial and clinical settings than in houses.
Safety flooring is sheet vinyl with slip-resistant grit built through it. Different job, different page. About safety flooring →