Tractor Service Manual describes how to take the tractor apart, how to fix it, and how to put it back together again. It is the manual that the factory furnished the dealer's service department, and was not sent or given to individual retail customers.
Tractor Parts Manual contains exploded views of all parts and assemblies on the tractor. It includes detailed pictures and diagrams giving you direction on assembly and dis-assembly. It also gives you a guide, with part numbers, for ordering replacement parts, and helps you to be much more informed when talking to the dealer.
Tractor Operators Manual, sometimes referred to as the owner's manual is the manual that came with the tractor. The manual that was given to the ultimate consumer by the manufacturer. It can be compared to the manual that comes in the glove box of a new car.