The main difference is in what the features each supports. An access point can only attach individual computers to a network. So say in my office, for example, I can put it in Access Point mode, and everybody can get on my network.

A router can connect computers on different networks. If say in the office, I wanted to pulg in a cable modem or whatever to get on the internet, I would have to be running it as a router, because the access point couldn't pass traffic from my side (the PC's or notebooks or whatever) over to the other side, the hotel network or whatever.

So if you are planning on sharing a connection to the internet with it, it has to be running as an router. If you already have an internet connection someplace with another router on the network, you can run it as an access point, but in your case you will need to run it as a router.