The Moderator Diamond that appears next to a moderators name when they comment. Do those stay after moderators have ended their term? or are those only shown for presently active moderators?
They only show for active moderators: if a moderator stops being a moderator, all of their past posts retroactively lose the diamond. Conversely, if a regular user becomes a moderator, all of their past posts retroactively gain the diamond.
The diamond next to a moderator's name represents that user's current status as an active moderator. When a user becomes a moderator, all previous posts, comments, close, and delete messages, even answers, questions, and comments from day one will be represented by that diamond. This is why so much emphasis is put on scrutinizing a user's past behavior during moderator elections.
With that said, once the diamond is removed, the diamond is removed across the board. In fact, if you look carefully enough, you can see some closed questions that only have one close voter, yet this person has no diamond. This is generally either a former pro tem moderator whose term expired when the site launched, a former Stack Exchange employee, or a moderator who stepped down for other reasons.
In short, if you see a diamond by a user's name, that user is currently an active moderator.