So they are "professional" because the are part of the standard career track that eventually leads to someone getting a formal "professional" qualification? That would suggest that an MBA is not a professional degree, although it is a vocational degree, because MBA graduates don't typically go on to become formally professionally qualified (e.g. unlike lawyers, medical doctors, etc.).
[NB I'm in the UK and while I know plenty lawyers/chartered engineers etc. I've never heard anyone talk about a "professional degree"].
No they are professional because they are required* as part of the license in that profession. To be an RN you have have to have a Bachelors of Science in Nursing. A CS major couldn't become an RN but an RN can become a software developer. It is the same for accountants, doctors, surgeons, etc.
Professional degrees are very specific and single focused. An MBA is just an MBA, no career requires it, but it is a nice to have. It is not considered a professional degree although many professionals do have it.
[*] and when I say required it is a felony to work in that field without the proper degree or license.
I didn't think UK CAs have to have a degree in accounting, I'm also pretty sure that you can become a CEng without an engineering degree, it's just very difficult.
I know that in law in Scotland you need two academic qualifications (a law degree, and a postgrad diploma in legal practise) then two years training before you qualify as a solicitor. However, if you want to go to the bar you only need a law degree - but then you have to do a specialised training course and then devil for a year before you can be called.
[NB I'm in the UK and while I know plenty lawyers/chartered engineers etc. I've never heard anyone talk about a "professional degree"].