Lithium-ion is an umbrella term that properly includes common cell chemistries like lithium iron phosphate (LFP), lithium nickel manganese cobalt oxide (NMC) and lithium nickel cobalt aluminium oxide (NCA).
It doesn't make sense to compare LFP vs. lithium-ion, because the first is a sub-type of the second.
Most commonly when people say lithium ion they really mean lithium polymer (lipo). Usually for the other lithium ion chemistries they will specify like you Jane (LFP etc).
You are technically correct - that's just how I've seen it casually used
Yes you can be a pendant about a topic to a degree that you manage to confuse even yourself, or you can understand the term is also commonly used to refer to the typical metal oxide cathodes we all are familiar with (NMC, LCO, NCA, lipo). From context it's really the obvious interpretation.
It doesn't make sense to compare LFP vs. lithium-ion, because the first is a sub-type of the second.