Expanding on the above, it's not so much to grant them moderation permissions (which are given from making them a moderator, as you say), but to do other little things like adjusting their user title/banner and giving them access to use staff-only forums.
I use the moderating user group to give the moderating permissions to all my moderators.
When I make someone a moderator I do so through the ACP and tick the option to add them to the moderating user group rather than adding the permissions individuality. Doing this means that:
I know all moderators have exactly the same permissions
It's easier (one tick box instead of many)
I can make a change to the moderating user group permissions (eg give a new permission) and immediately all moderators have this (rather than having to add it individually to each moderator)
Basically the moderating user group permissions I use for all Super Moderators. I'd only use the individual moderator permissions in the ACP if I needed a moderator to have different permissions from the others or for Forum Moderators (who moderate individual forums).