The spindle rotates inside two bearings at either end of the quill; these are the quill bearings and there are two. The spindle extends up through a sleeve with internal teeth that match those at the top of the spindle. This is the drive sleeve that runs inside two more bearings separated by a spacer. The top of the sleeve has a taper that mounts the drive pulley. As the pulley turns, it turns the drive sleeve that, in turn, drives the spindle. That is how power is transmitted to the chuck.
When you change bearings, you should change all four - two quill bearings and two drive sleeve bearings. Pull the bearings and buy the equivalent bearings but I suggest you use sealed bearings, not shielded ones. The grease in sealed bearings last longer. I also suggest you buy deep groove bearings from Nachi or NSK. Deep groove bearings can sustain high axial and radial loads and quality Japanese bearings are worth the small extra cost.
My 30 year old Craftsman drill press has Nachi bearings that are at least 8 - 10 years old by now and it still holds about 0.0005" TIR at the spindle despite frequent use. Most folks worry about how accurate their drill chucks are but the primary source of accuracy in a drill press are in the bearings, all four of them.