rearranging plumbing in a concrete floor

I have two very very small bathrooms that I would like to combine into one. This would require rearranging the fixtures. My question is this... Can I interchange the drains? Use a shower drain for a new toilet or vice versa?

Also, the house was built in the 1960's so there is no concrete around the shower or tub drains, only dirt.

drains

No, you cannot interchange a toilet and a shower. In fact, from your inquiry, I would suggest you contact a plumber because there will be a LOT of piping which has to be revised to do what you intend to. In fact, you will probably have to remove most of the existing and start over.