Replacing my distributor first time

What you are missing is an intermediate shaft

This is driven by the camshaft, and the upper part of it engages the distributor, while the lower part engages the oil pump
(The flat spot you see on the bottom of the distributor goes into this shaft)
So when you swap distributors, the intermediate shaft stays in the engine

If you ever change over to a high pressure oil pump you may want to replace that shaft, but at this point I wouldn't worry about it