The North American numberig plan looks like +1-AAA-BBB-CCCC Where AAA is the area code and BBB-CCCC is mostly meaningless. There are a few special area codes like 8xx for toll-free calls (the classic 1-800 numbers that businesses often use) but no prefix dedicated to mobile.
When I moved to Ireland I thought it was weird that mobile numbers were identifiable. Especially since I had a Google voice number which looked like a landline which really confused people and websites. "Trust me, just text it. It is fine."
> Do you get a new number if you move
I don't know about the US but this used to be common in Canada. Many providers would consider calls to different cities long distance and charge extra. So if you moved it was "polite" to get a new number so that people could call you for local rates. For example I went to university in Ottawa and changed my Toronto number so that people didn't have to pay long distance to call (even though it is the same province, about a 5h drive).
However this isn't really the case anymore. In the US and mostly in Canada country-wide calling us pretty standard so most people's mobile number will reflect where they grew up, and they will carry that around for the rest of their lives.
> and then change to a different provider?
Usually not. You can ask your provider for a new number in a different city and they will issue it. Most Canadian providers are country-wide so you don't need to switch provide if you don't want to.