Roy Smith wrote in
:

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.

Admittedly, before this thread started, I was not aware that ASEL rating on a
Flight Instructor certificate was not a prerequisite for the Instrument
rating, like on a Private Pilot certificate. That being said, I don't think
my lack of this particular knowledge was caused by the use of the term CFI
vs. CFII. However, it probably would have been clear if the typical
discussion included 3 distinct abbreviations: CFI-A, CFI-I, and CFI-AI.