A litigator is a type of lawyer.  On television shows most lawyers are litigators.  They are lawyers who represent clients at criminal trials or in private lawsuits (Company A sues Company B or Mr. A sues Mr. B).  Some lawyers might specialize in criminal litigation, others might specialize in business litigation, such as contract disputes.   

When we refer to a lawyer as a “litigator” we are referring to the lawyer’s specialty.  There are other kinds of lawyers besides litigators.  Some lawyers specialize in transactional work such as when one company merges with another company.  Other lawyers might specialize in family law, tax, or intellectual property.  Television and movies usually have trials (because trials make good drama) so that is why most lawyers you see on screen are litigators, not transactional specialists.  

Some lawyers have more than one specialty.  A lawyer with a general practice could do litigation 50% of the time and also help people with real estate transactions and estate planning with the remainder of his time.