Administrators (admins) typically have full access to the website and are able to make any modifications to all members and any content on the website or software that associates an account as an administrator.
Moderators typically have less access and are usually only able to moderate some content such as member posts. They are able to delete them and more. Depending on the amount of power given to a moderator by the administrator, the moderator may be able to also ban a member.
On the website I am making:
Administrator (admin) privileges:
- Edit user info (name, email, picture, location, bio, etc.)
- Delete users from the site
- View feedback submitted by users
- Manually add a new user from the Admin Center
- Anything a Moderator can do (see below)
Moderator privileges:
- Suspend users
- Edit questions (title and body)
- Remove questions and answers (if they abuse TOS or guidelines)
- Remove comments (if they abuse TOS or guidelines)
- View reported posts by users
- Change the category of a question
- (there's probably more that I'm forgetting about :P)