As Gary said it varies from country to country. In the UK if you work for a national government department or agency you are a 'civil servant.' If your job is providing a government service in general (so that would include things like doctors, teachers, the police, local council workers etc) then you are a 'public sector worker.' Those jobs are known by the collective term 'public sector jobs.'

That probably varies a bit from country to country. Here it would probably be a public servant. Although, having said that, most people would think of a public servant as someone who works for a government department, and might not include the police in that. And here - people who work for the city council would not be called public servants, but council workers.