Superficially, the difference is that a pillow-top mattress has extra layers of wadding materials (foams etc) stitched on to the top of the main body of the mattress. The resulting extra layers looks a little like a pillow stitched to the top of the mattress, hence the name.
A euro-top is a more recent development. It also consists of extra layers of wadding materials added to the top of the mattress, but inserted under the outer cover of the mattress to create a box like structure with square edges.
Opinion is divided on whether the difference between the pillow-top and the euro-top is anything more than aesthetic. In principle, if the mattress is well constructed with good quality, resilient (returns to its original shape) layers of padding sewn together with a good quality, resilient outer cover, then the euro-top should retain its shape for longer than the pillow-top. When a mattress is well made, the outer fabric of the mattress stretched over the edges of the euro-top ought to behave like the material of the elastic surface of a trampoline, returning to its original shape when the weight of the sleeper's body is removed from the mattress surface.
in the UK, Test and OkoTest in Germany indicate that a well-made euro-top mattress or mattress without a pillow-top is likely to retain its shape longer than a pillow-top. However, such an effect is unlikely to be observable if non-resilient extra layers of wadding and non-resilient mattress cover are used. Well-made, well-tempered mild-steel springs and blocks of natural latex continue to be the most resilient materials used in mattress making.