The different cell phone providers such as T-Mobile or Verizon use different cell phone technologies for their cellular network. This has a bearing on the type of Smartphone that you purchase as phones designed to work on one network generally will not work on the other. (In the United States, you usually purchase your Smartphone from the Cellular provider so compatibility is not an issue) The type of phone you have will also determine if it can be used when travelling abroad.
Brighthand has a non-technical article describing the differences between the two major technologies which can be found HERE.
The above article also has a link to another FAQ that discusses the different data transfer methods used on the above networks.