If I drill a hole with bit diameter “x”, what is the diameter of the resultant hole? How is the bit diameter related to the actual drilled hole size? I'm sure the latter is slightly larger, but by how much?

The diameter of the hole drilled depends on the material and your operation. If the material is soft, the diameter of the hole will be a little larger. If the material is hard, the diameter of the hole is slightly larger. If you do DIY job, you can ignore the larger size. The operation means if you hold the drill press tightly, the hole size will not be larger. If you hold the drill press shakily, then the hole size will be a little larger. So it is hard to say the exact larger size.

And also the straight shank drill bit and hex shank drill bit is different for the holes. Normally the holes drill by hex shank drill bit will be larger than the ones drilled by straight shank drill bit.