The missing link in all this is the fact that in the UK a 'professional engineer' is one who has 'Chartered' status which is closely guarded by the senior engineering institutions and these days requires not only an honours degree, but one from a very limited list of universities.
I write C.Eng M I Mech E after my BSc(Hons) on my business card. I can sign passport applications and various other legal documents (I don't think I can marry people though).
The problem in the UK has always been that unlike some countries the word 'engineer' is not protected. Repeated attempts to get legislation to ban the use of the title by non-chartered people have failed. So a plumber can call himself a sanitary engineer if he likes. No wonder the public are confused. In Germany and other European states the title is protected and use of it by those not entitled is breaking the law.
When bidding for US DoD contracts in the defence companies I was in, the number of professional engineers (ie Chartered - PE to them) allocated to the job was a matter of great importance. If you didn't have enough you would not win the contract.
When I worked in Germany I was always introduced as Herr Diploma Engineer ... so as to make the distinction clear - the Germans were very fussy about rank and titles.