Is a Research Assistant/Associate in the United Kingdom equivalent to a Post Doctorate elsewhere?
Just to clarify, "Post-Doc" typically is short for "Post-Doctoral Researcher", not for any position in academia after finishing one's PhD. It refers to the first research position one would get after the doctorate.
In that sense yes, a Research Assistant/ Associate is typically a Post-Doc position in the UK but there is significant variation in the contract type, payment, duration and situations. Think of it as a blanket term for an entry-level research position, but the contract could be anything. A bog-standard Post-Doc is tied to either a project or departmental funding, meaning that at the end of the project you are out of a job and continuation is subject to the progress of the project and whether funding is available. It is fixed time (ranging from 6 months to 3 years, more commonly 1-2 years and renewable at the discretion of the university), but you should become familiarised with how you fulfil the requirements for a permanent contract. In the UK, this is possible after 2 years of continuous employment on renewable contracts (e.g. two consecutive 12-month contracts) or 4 years of employment on renewable contracts but with breaks (e.g. four 9-month contracts with 3-month gaps between them). The difference with a Research Fellow (RF) is the wage, which is often higher than an RA, and that RF contracts refer to a permanent position more often.
Unfortunately, the above do not always hold in practice and you should always read the job description carefully to see to what the "Research" bit in the title refers to. There is also a trend to harmonise naming with the US system (Assistant/ Associate Professor etc) which further complicates things.
The career equivalence between the three tracks (research only, mixed, teaching only) is Research Fellow, Lecturer, Teaching Fellow, which typically and ideally refer to permanent positions with comparable workload and responsibilities. This is not always the case, as RFs are often not permanent and TFs are paid less. Prior to those, you have Research Associate and Teaching Associate, with nothing for a Lecturer equivalent.
Now, for "post-doc" as in "any academic employment after the PhD", you are looking for both research and non-research positions. This includes everything: RA, TA, Lecturer (a long-shot at present), RF, TF.