A Milanese mesh is a woven sheet of steel: it takes the shape of the wrist, sits flat, and slides under a cuff without catching. A link bracelet is a chain of solid pieces: it holds its own shape, catches light in facets rather than as a sheen, and stands slightly off the wrist. Mesh is the quieter of the two and the more comfortable for most people; a bracelet is the more substantial and the easier to live with, because links come out at home with a pin pusher while mesh needs a tool and a steady hand.
Sizing is the part people find out afterwards
A link bracelet arrives too long and is meant to be shortened; a jeweller does it in minutes and a pin pusher does it at home. Mesh usually slides on a clasp along its length, which sounds easier and is fiddlier to get exactly right, and some mesh has to be cut. Worth knowing before rather than after, because a watch that does not fit is a watch that stays in a drawer.
Neither of these is a swimming watch
Both are dress watches at 30 to 50 metres, which means splashes and rain rather than a pool. Steel straps also trap water against the skin, which is more of an irritation than a risk. If a watch needs to go in the sea, that is a different category entirely and neither of these is pretending otherwise.