However this is a case where they appear to be forced to overlap on occasion.
Overall, though, you are stating more directly what I myself said. This issue appears to be primarily centered around businesses. My take: If you own a store that says "no guns", then fine, I have a judgement call to make. If I'm carrying, do I go in unarmed? Or do I take my business elsewhere?
If I'm not carrying, then I still might not patronize your establishment out of principle. As I said, let the market decide.
If it's your own home, your rules most certainly apply. As does my own freedom to disarm and be welcome, or leave.
My parking lot is no less my property than my home is, my rights are not lessened by the fact that I don't sleep in my parking lot.
There is no overlap of rights here, there is however a willingness by "conservatives" to violate a very basic principle of conservatism.