There can be differences in coverage between the native network of AT&T (or Verizon or Sprint) and that of an independent service that buys time from them to use their network. The differences occur when the primary carrier has roaming agreements with other carries that are not passed through to the independent, a common thing. Say that ATT makes a roaming agreement with XYZ Cellular, a small regional carrier and they agree to carry each other's calls for free. Then AT&T makes an agreement with Straight Talk (or Tracphone or...) to sell them time on the ATT network. That agreement gives access Straight Talk to the ATT owned towers but generally does not to the additional networks with whom ATT has roaming agreements. Generally, Straight Talk has to make their own agreements with XYZ Cellular to carry their traffic as well.
A similar difference in coverage can happen with voice vs data coverage - a roaming agreement may provide voice service but no data, or vice versa. That's not as common as it once was, but can still happen.