PA is a very loose term - arguably invented when 'secretary' started to become (incorrectly IMHO) a demeaning term - or at least one that implied your role was simply copy-typing and answering the phone. It can be just that, but either term could just as easily be used for someone whose role encompasses a vast range of admin and organisational tasks. From client handling to scheduling travel arrangements and the smooth running of an office.
What is a given is that great communication skills are vital, both on a practical level - typing and shorthand, computer literate - and also good use of language, both written and spoken. Languages are often a bonus, or even essential depending on the role.
Whether you actually need a degree for this will depend entirely on the specific role. Some may ask for something general - or even any degree, others may require a certain subject - typically languages.
PR, is again, hugely communication led, but again subject specific courses may help, but often you will find that what separates the best PRs is not educational but experience - typically a journalism background and a huge network of contacts.
In either case, try looking at the job vacancies currently advertised (impossibleprincess, you are in the UK so the best place is The Guardian on Mondays and Saturdays). See what they are asking for.
