The terminology is fairly ambiguous. Back in the day "moderating" frequently referred to using the 10k tools, and "♦ moderator" was for elected mods. Now "moderators" typically refers to ♦ mods. You'll occasionally see "pseudo-mods" used to refer to 10k users as well, but that's pretty much died out too.

As for privileges, see [What's the difference between a moderator and someone who has access to moderator tools?](https://meta.stackexchange.com/questions/136890/whats-the-difference-between-a-moderator-and-someone-who-has-access-to-moderato) on the main meta. In theory 10k users can do everything that doesn't require access to sensitive data. ♦ mods don't need to vote to perform user actions, and have a few extra things they can do that users can't do at all. They also have access to a bunch of random site data, which is the reason for the [moderator agreement](http://stackoverflow.com/legal/moderator-agreement), but the hope is [regular users can do almost anything](http://blog.stackoverflow.com/2009/05/a-theory-of-moderation/)