I think there will be a lot of regional variation. Here "civil servant" isn't used that often but I think of it as any non-elected government or government-like employees except for the police and the military. It's not restricted to administrative jobs, so could include jobs like mail carrier, social worker, inspector, nurses at a public hospital etc. That is, people who wouldn't be considered "bureaucrats". Bureaucrat refers to someone doing administrative work. It's a word not often used to described oneself, because it can have a negative connotation (someone who is interested in paperwork and out of touch with the people).

I agree with Nico. I can’t think of an example of general administrative use of the word bureaucrat that he’s thinking of though. I’ll also add that a bureaucrat implies some amount of authority to make decisions. Civil servant is more general in that way in that it could be someone doing entry level government work or it could be someone in a high office.

Thank you Nico

civil servant is a person that works for the government, or even more specifically, in Civil Service a bureaucrat can also mean someone working for the government, but it's less specific, it can also describe people that have general administrative work. Important difference is that a bureaucrat can have a negative meaning- someone that loves strict schedules and rules too much.