I would think that since your physical self is across the state line in the first example, your state would not be able to regulate or tax your behavior- You are under the protections and rights of the neighboring state.
However, in the second instance, your physical self has not crossed the state line, and is therefore subject to the laws of your home state.
That is the significant difference, as I am sure you will agree.
In regard to interstate purchases by mail order, there is some discussion about which end gets to tax the sale- To my knowledge, your obligation is to the state of delivery, or in most cases, the state that you are in.
I have no idea how that actually works, as Montana (my state) has no sales tax. I do know that I do not pay sales tax in the originating state when purchasing on-line, or at least not to my knowledge.
If that is correct, that bolsters the idea that the gambling taxes would be the right of the state in which your physical self resides.
And that is the significant difference that decides who has the authority to regulate your gambling activities, and who's responsibility it is to enforce those regulations.