Litigator is just a fancy word for trial attorney. Litigation is the fancy word for trial preparation and trial work. Not all attorneys are litigators. But all litigators are attorneys.
What makes a trial attorney special is that they have been to trial. In todays multi-media fast paced world, most folks think trials happen all the time. They do not. And as less and less cases go to trial, fewer and fewer attorneys are actually litigators.
If your case fails to negotiate/settle, then you want someone who has been to trial. You don't want someone who is figuring out how a trial works when you have so much at risk. Much like you would not give the keys to your car with your family inside, to someone who has never driven and tell them to take a spin on the freeway/interstate, you should not trust your business or your personal interests to someone who does not know what they are doing.
When you are looking to hire an attorney, you should ask about their experience. How many cases have they taken to jury trial and if not, why you should trust your case to them if they have settled all their cases.