Be careful when you see adds especially on AI websites that advertise "lawyers". On in particular has come to mind recently. Some people call themselves "Lawyers" simply because they have a Law Degree or even less in some circumstances. Anglo French Property Lawyer springs to mind .
The Legal Services Act suggests that lawyers are:-
Solicitors regulated by the SRA.
Other lawyers in that act are defined as:-
barristers, notaries, legal executives, licensed conveyancers, patent agents (patent attorneys), trade mark agents (trade mark attorneys) or law costs draftsmen.
The SRA states a lawyer is an legal professional which is recognised as such by the SRA and thus I assume all the professionals mentioned above in the Legal Services Act are recognised as 'lawyers'.
Look at the definition of 'other lawyers' here:-
Solicitors Regulation Authority - Legal Services Act - glossary of terms
All these professionals are 'lawyers'. However, when describing yourself you should use the exact professional description, e.g. I am a solicitor, I am a barrister, I am a trade mark attorney etc, etc.
Barristers obviously have rights of audience before the courts, as do trade mark attorneys and patent attorneys. Solicitors and all the aforementioned professionals can become judges.
The term 'lawyer' is slightly nebulous term in general parlance but if you want to argue who is a lawyer, then I believe that the definitions within the LSA should be followed.