I've changed username, because it may become pretty outing what I do for a living.
There are a few reasons why people who have Limited Companies and may say they are self-emoloyed, but I'll name only 2:
1 Just because it's easier. When people describe themselves as a director of a company, generally, unless people understand, they get a whole ton of questions. Some people think "companies" are only for shops or big corporations and you have to employ loads of employees. That's not the case, you can be a company and it be only you as the Director who works in it.
So, to make life easier you just say "I'm self employed ", as most people understand this
2 Some people dont understand that they are no longer self employed, and are now shareholder and Director of a Ltd Company.
To give you an example, I was talking to this gentleman who was an electrician. I was asking about his Dividends, PAYE salary etc.
He genuinely had no idea what I was talking about. He said, he doesn't understand the whole thing. All he does is every month send his accountant detail of how much he's earnt and his expenses, and his accountant does everything. He just signs the paperwork, pays what the accountant tells him to pay, and trusts everything his accountant is doing.
He didn't know his accountant had structured a Ltd Company, as far as he was concerned he was "self-employed".
I suspect your friend's DP has fallen into no 2.
I suspect what's probably happened is she's trusted whoever was sorting this, signed some forms, but didn't really understand what was happening.
(Nb, there's no judgement from me, who fall into no 2. Tax can be complicated, so maybe dont know that they should be asking what is happening wuth their earnings etc)