In American English, "lawyer" is less formal, "attorney" is more formal. You might occasionally here "counselor", but probably only in court. (since attorneys/lawyers "counsel" people in legal matters). There is no other difference, in the States.
With few, technical exceptions (such as patent law), an attorney/lawyer can handle just about any type of matter in the States. In England, you need either a solicitor or a barrister, depending on whether you have to appear in court.