Hi Mona,
Yes, "civil servant" and "bureaucrat" means the same people. People who work for the government.
There are small differences in the two phrases, though. "Civil servant" sounds more positive, and "bureaucrat" sounds more negative. So, if you like people who work for the government you might call them civil servants. If you don't like them, you might call them "bureaucrats."
Also, "bureaucrat" implies office work... but a "civil servant" could be anyone who works for the government even if they do not work in an office. A police officer, a fireman, a judge, a school teacher, social worker, a city mayor.... these are all civil servants. But when we say "bureaucrat" I think of someone who works in a government office. Maybe like a tax collector.