Yes, there are different licenses, because the types of flying, the way you interact with other aircraft and the rules in which you can operate are very different between civilian and military operations.
The one thing that applies to all licenses is the number of hours you have done. In order to obtain a license, you need to have flown a set number of hours in certain conditions (e.g. 100hrs, including 25 in IMC for certain countries' instrument requirements). The number of hours required for a full ATPL (Airline Transport Pilot's License) is massive, so many would-be airliner pilots are sitting with a CPL/IR (Commercial Pilot's License / Instrument Rating) and all the exams done for the ATPL, but not enough hours in an aircraft for the ATPL to be valid. This is known as a "frozen" license and you can guarantee that the pilot will take any stick time he can get to achive the minimum hours.
Even though military flying hours have been consistently slashed across the globe following the end of the Cold War, most military pilots still leave the service with more than sufficient hours to hold a full ATPL, so it's just a case of pass the exams, get the medical and - most importantly - a type rating for the airliner type you want to fly. You can have thousands of hours, every license it's possible to get, but if you want a job flying an A320 and don't have an A320 type rating, you won't be flying one.
It's a well known fact that until you get right up the top, flying for a living costs more than you bring in doing it. You have to do it out of love, not to get rich. Only four bar Captains for big airlines are paid the big bucks and the military is no longer a guaranteed route into that position.