Moderators are responsible for trashing spam, moving topics to correct sections, and not much much else tbh. Full mods have access to also warn users. D team engage in reporting users who are breaking forum rules (spammers, shills, plagiarists, etc), so that mods can give appropriate warnings, strikes, membership groups, etc. There is an obvious overlap but not all mods are part of d team, and not all d team are mods, for the reason that there is simply an overlap in roles/duties but not a requirement to fulfill all criteria to be either.
That said, it's natural that should any d team members want to become mods, they'd be granted such responsibilities (for the right reasons) without much after thought.
Baring in mind that it's primarily based on activity in such section that a user wishes to moderate...