I found the following on a Verizon web page entitled "Determining Verizon Wireless Service Coverage":
"When the roam indicator is flashing or the banner display reads Extended Network, home airtime rates still apply, but additional features and services may not be available.
"When the roam indicator is solid or the banner display reads Roaming, roam rates apply and digital features and services are not available."
The distinction seems to be mainly one of price, but also of services.
As far as I can tell, AT&T has only one sort of (domestic US) roaming, but Verizon has two different terms.
As far as I can tell, since AT&T doesn't charge for domestic voice roaming, there is no switch to enable or disable it. You can switch data roaming off and on.