When your contractor talks about "recoating," that means he's going to lightly abrade the finish on the floor and put a new coat of finish on, or he's going to use a chemical recoating system that can put a new coat of finish on the floor without any abrasion.
When he says "re-sand," that means re-sanding. One big indicator that tells you if you need a recoat or a re-sand is how much finish is left on the floor. If there are bare spots on the floor, where there isn't any finish left, you can't just recoat. A floor with bare spots has to be re-sanded.
Beyond that, recoating versus re-sanding is largely a matter of your expectations. If you want your floor to look like new, you will need a resand. If you can live with still seeing some scratches, dents and other damage to the floor, recoating is probably the way to go. Be aware, though, that recoating can seem to highlight the imperfections that are left in the floor.