How can I select and move only one primitive? I have a model which currently consists of two basic primitives.  I want to select and move only one of the shapes, but while in object mode it seems to be treating them as one object.  Must I switch to edit mode and select every vertex of the one primitive or is there an easier way?

Edit:  I should note that my end goal is to carve one shape by doing a boolean difference between the two.
If you have joined 2 objects then you will need to access each one of them by going to Edit Mode

Once you are in Edit Mode, hover your mouse over the primitive you want to select and press L.

You will be able to select a single primitive of your choice.