[Networking] MrObvious:
I'll try to make it simple for you. There are really two types of cell networks (not counting LTE, since all carriers are using that now here in the US): GSM and CDMA.

CDMA is what Verizon, Sprint, US Cellular, MetroPCS, Cricket, and maybe other smaller carriers use. It is based on a serial number called a ESN on older phones or MEID on newer phones (since the late 2000s). That serial number is burned into the programming of the phone on the ROM and cannot be changed very easily and is illegal to do so supposedly. There are two types of CDMA technology in use today, 1xRTT and EVDO (older analog was phased out a few years ago). 1xRTT or 1x as it's abbreviated, is a "2G" technology that allows for packet switched voice and SMS traffic, as well as very very slow data speeds (think 56k dialup). EVDO is strictly for data (the voice part was never added because they didn't want to pony up the cost of it) and is used in Rev 0 and Rev A EVDO. Most Verizon/Sprint 3G is Rev. A EVDO. It hits a max of 3.1Mbps down and if you get a call or text message, it drops to 1x and the 3g is suspended, unless you have a radio that can do both at once (HTC Thunderbolt). You activate by serial number and a bad ESN means they didn't pay their bill or it was an insurance claim on a lost phone and they are blacklisted.

GSM is a technology essentially where it uses a little plastic and electronic card called a SIM card. T-Mobile and AT&T are the two major carriers with this technology. There are several revisions of this technology in use today, GRPS, Edge, and various UTMS and HSPA versions. GRPS is analogous to 1xRTT in terms of speed, and Edge is in between and gives up to 250kb/s down, technically a 3g technology, although not feeling like it. UTMS, HSPA, and WCDMA all refer to a similar type of technology which is what is used by the 3G level of service of AT&T and T-Mobile (fake 4G on T-Mobile). It goes from just faster than Edge to DC-HSPA 42Mbps down speeds and allows for simultaneous voice/data (Edge and GRPS are either data or voice, not both). Your phone number is tied to the SIM card and this technology offers an advantage of if your main phone craps out, you can store your contacts on the SIM and just put it in another phone and still have service.

Roaming and tower authentication are completely different in GSM vs. CDMA. CDMA uses what's called a PRL (Preferred Roaming List) to determine which towers to authenticate to essentially, and sets priority. Some people will "hack" the PRL by changing it so for example if they have Sprint and their tower has the crappy 3g speeds, they roam on Verizon since they have unlimited roaming and get Verizon's better 3g speeds. GSM roaming is set per tower or location on the SIM card, and is a pretty static value dependent on the carrier. Roaming is only if they allow it depending on your plan and location (like T-Mobile prepaid will not roam on AT&T, but postpaid "Uncarrier" plans will).

So what you have is probably a tablet based on the data that gets EVDO service and probably 1xRTT and maybe LTE. If you have it on a phone plan and not a tablet plan, it's probably a Note 2 or something which is just really a phone from what it sounds like if you use Bluetooth. CDMA carriers will only use their devices and lock down ESNs to what they sell, so you can't buy a device from Sprint and put it on Verizon. The exception to that is sometimes prepaid carriers will let you "flash" the phone to their service but don't guarantee the results and don't support it. Examples include Cricket, MetroPCS, Page Plus, and I think Virgin Mobile or Boost *might*, but don't quote me.

LTE is a newer technology which isn't technically 4G yet since we haven't seen speeds here in the US on current LTE revisions of over 100Mbps, but they do have the ability with the right equipment. It uses SIM cards so you will see newer Verizon/Sprint devices actually use SIM cards for service (which is superior as noted above), and have an ESN so it can fall back to 1x or EV. The plan is to eventually roll out LTE to all towers and if you have a LTE device, you use LTE for voice and data (VoLTE), but all carriers don't have LTE on all towers so they fall back to HSPA/Edge or 1x for voice for now. They probably have dual radios like the HTC Thunderbolt and use both at the same time but LTE is still a maturing technology and has a lot of potential.

I hope this helps.

Edit: I forgot to add, for the smaller prepaid plans, you have to look at who they are based off of. Most of them just use a parent network from one of the 4 big carriers (Cricket being the exception, they have their own towers and roam on Sprint if you leave native coverage). I know Page Plus uses prepaid Verizon towers, but for the most part you won't get unlimited uncapped data on Verizon unless you keep your old $30 grandfathered plan. If you switch to a limited data plan, say bye bye. Honestly if you don't want to pay Verizon prices (I don't blame you), and you have the availability for it for coverage, T-Mobile or Sprint have good options. T-Mobile's network where they have 3g/4g is way way good. They just deployed equipment on their towers that's above everyone else with new NSN antennas and the LTE revision is LTE-A I think (check what Milan posted on Howard Forums for sure), but it's high dollar equipment that isn't cheap. Also they are upgrading the backhaul on their towers and most people are pulling between 10-20Mbps on DC-HSPA and 15-30Mbps on LTE. Milan got about 25 Mbps in NYC on T-Mobile LTE so they are a really good way to go and you can get an unlimited plan for $70 a month prepaid. Also, you can get a 5GB/100 min/unlimited SMS plan for $30 from Wal-Mart/tmobile.com.