The carbodimide mechanism is thought to be as follows. The carboxylate group attacks the electrophilic carbon of the carbodiimide and a proton is picked up. The intermediate is attacked by another carboxylate molecule and forms a tetrahedral intermediate. This breaks down and the leaving group leaves and then tautomerizes to give the anhydride and the urea byproduct. Each of these reagents has advantages and disadvantages.
Many compounds have different abbreviations.
Different compounds may have the same abbreviation. It may differ between different fields. Be safe and be sure. The advantage of EDC over some of the others is that the resulting urea is very water soluble and can be removed just by extraction. This is a two week lab.