Judah wrote:

I'm confused. Doesn't CFI stand for certificated Flight Instructor?

The problem with the terms "CFI" vs. "CFII" is that it leads to the common
confusion that a CFII is a "more advanced" rating/certificate/whatever than
a "just plain CFI". That's not true.

I hold two certificates from the FAA. One is my commercial pilot
certificate, the other is my flight instructor certificate. Each of those
certificates has ratings that go along with it. On my pilot certificate,
I've got "airplane single-engine land" and "instrument airplane". On my
instructor certificate, I've got "airplane single engine" and "instrument
airplane".

What makes this confusing is that on the pilot certificate, having the
airplane rating was a pre-requisite to getting the instrument rating. This
is NOT true for the instructor certificate. While it is common for an
instructor to get the airplane rating before the instrument rating, it
doesn't have to be that way, and in fact, it's not terribly uncommon for
people to get the instrument rating as their initial instructor rating.

If for example, I had done that, I would have been able to give instrument
instruction (i.e. towards an instrument rating or an IPC) in an Archer to a
pilot who already had a single-engine land rating on his pilot certificate,
but I would NOT have been able to give somebody primary training or a BFR
in that same airplane until I also went out and got an airplane rating.

Leave it to the FAA to invent such a bizarre and complex system.