Pay closer attention to the US Cellular maps. When you don't make a distinction between owned network and roaming, Verizon and US Cellular show the same maps, because for voice both use CDMA 2000, and where US Cellular has no network, You roam onto Verizon, and vice versa.
Data roaming doesn't always work the same, so there are different maps for data.
I can't buy Verizon where I live because there network is not where I am. At that tier, the CDMA 2000 carrier is US Cellular, which I can buy. Verizon phones work here, they use US Cellular's towers and connections. They used to use Dobson, a lower tier carrier, and tried to buy Dobson, but AT&T outbid Verizon on that sale, and expanded into Dobson territory instead, so they no longer need to roam onto T-Mobile in this location.
If you are in US Cellular territory, use only voice, or do not want data when you travel, go with US Cellular. If you travel, want data, and can buy Verizon, buy Verizon. If they don't have towers where you are, they won't sell service (that's how the FCC manages licenses, matching service areas to subscriber addresses).
That's if you are hooked on CDMA as a technology. If you will be happy with GSM (used globally) then AT&T is the big guy and T-Mobile is the little guy filling in most of the spots where AT&T is not licensed to have subscribers, though there are still also a few lower tier GSM providers, in very small areas, both may use to fill in by roaming.
For data, as we move to LTE and beyond, much of the network is yet somebody else, and the major providers buy the service from the technology owner, whether using CDMA 2000 or GSM derivative tech for voice and slower data services.