I think you've just answered your own question.

Choosing of either terms to describe a particular long haired cat pretty much arises depending on who you're talking to. I noticed if the person is like an expert on cats, DLH will be more commonly used and non-experts, Persian X la, Persian mix la, long-haired Persian la, etc. I think so la, normally general cat lovers when you tell them, "I say, that's a nice looking DLH you got there". Then they'll go, "Ya...ya......DL...what?".

When people ask me, I normally just tell them Persian X.

wooz...