NAD+ and H+ are not the same.
NAD+ is an electron carrier. Reactions in metabolism oxidize food molecules and transfer those electrons (along with H+) to > NAD+ which is what forms NADH. Now, NADH is the reduced form of NAD+ and NAD+ is the oxidized form of NADH.
H+ on the other hand, is a proton. It is a hydrogen atom that lost it's electrons. So when you see NADH + H+, that means that the reaction removed 2 electrons and 2 H+ from the compound.
