A valid Pilot's Licence (including valid Medical) entitles the holder to act as a Pilot.
Does this mean they can legally fly any aeroplane they want?
No. They also need to be qualified to fly a particular aircraft by holding a valid relevant Class or Type Rating, and also possibly requiring Differences Training to be have been signed off.
A valid FI entitles the holder to Instruct.
Does this mean they can legally instruct for anything they want?
No. They also need to be qualified to give a type of instruction by holding the relevant Instructional Privilege.
What's the difference?
Good job there isn't an exam in the FIC and instructor renewal about all the different flavours available. Their would be an instructor shortage pretty quick.
During an FIC the candidate certainly should be taught, and quized on, the Instructional Privileges they are attempting to have granted. For every Renewal an FI will need to attend either a Seminar or a Test with an FIE (possibly both). Instructor requirements and Privileges should be reviewed at these (even if not tested).