Connecting GSM to Internet IP address

Hello all,

I don’t have an electronics background but I’m developing a proposal for a wireless device. I know the feature set it needs but I want to be able to speak more intelligibly about the technical side of it.

This device will periodically send SMS messages with data to a web server for display on a website. If the device communicates over a GSM cellular network, what “number” is it dialing to upload data to a website? Is that the IP address?

Additionally, is an IP address unique to a specific computer or to a network in general? i.e. if I want the data sent to my computer specifically, will that occur regardless of whether I’m using my home network or using the wireless network at Starbucks?

Thanks and all the best