How much knowledge is expected of a PhD applicant as compared to a postdoc or a research assistant? My understanding is that postdocs, research assistants (which I understand are master's level analogues of postdocs) and PhD students are all paid positions except for self-funded PhD which I hear is rare, but regardless, PhD students like postdocs and research assistants are expected to assist with the specific research that the professor is doing.

But, considering that a PhD studentship is the pursuit of a degree rather than the application of acquired knowledge from a degree, how much is expected of background knowledge for a PhD applicant?



There was this quora post that I can't find anymore that asked why professors took on PhD students to assist with research instead of hiring a research team or something. I was supposed to link it as an introduction.


Update: I found the question! Why would a professor want a Ph.D student instead of a research staff? What are the advantages and disadvantages?


Anyway, my question is different from the following because I'm asking specifically for PhD students relative to postdocs or research assistants.


How much is expected to know before starting a PhD
What kind of knowledge is required to do a PhD?
How can an undergraduate student conducting mathematical research with a professor expect to contribute?




I'm going to use math for examples.


If I know elementary topics of complex analysis, abstract algebra, algebraic topology, algebraic geometry and differential geometry, can I apply as a PhD student of a professor who specializes in complex analysis? Complex geometry? Functional analysis? Differential geometry? 
For location: I don't mind if people post an answer for US or Europe, but in case I really need to say: I live in Country A, which is somewhere in the middle.
I will only attempt a partial answer here as your question is a bit convoluted. Doctoral students on the first day, are expected to know less than a post-doc or research assistant on the first day. But they are expected to know relevant things. How your specific case would be judged would be up to a specific judge (i.e. a potential advisor). 

But note that universities (as opposed to commercial/industrial labs) have a dual purpose. It isn't just to support the research interests of the current faculty, but to also educate the next generation(s) of scholars and researchers. Without that second  purpose there would be no need for graduate students at all. But then scholarship would end in a generation or two. 

Universities are long term contributors to the future and take the role seriously, both in research and teaching. 



The other links in your question seem to be pretty good for answering your other concerns.