Cell phones were a division of AT&Ts overall business and then at some point they spun that out into Verizon. And then later they got back into mobile/cellular via Cingular, essentially competing with their old selves (Verizon).
[0]: https://www.marketwatch.com/story/sbc-to-acquire-att-in-16-b...
But all the baby bells were just operating separately in name only in many regards. My mother—in-law worked for AT&T or one of the baby bells her entire career, across multiple states and systems. It was a lot more similar than a lot of people realize. Once wireless became a thing and being regional became much more arbitrary (because a local telephone provider doesn’t matter in the age of nationwide wireless), the re-unification made sense.
And aside from MCI and Sprint, neither of which had good histories, or the German-government propped up T-Mobile (American T-Mobile was largely subsidized by Deutsche Telekom in its early years, first launching nationwide as VoiceStream), no one was able to make a go at competing against the bells anyway. The fact that AT&T and Verizon still dominate the industry and that both used to be the same 40 years ago really isn’t much of a surprise.
I’m generally a fan of deregulation, but the phone situation shows that breaking up the monopolies really didn’t cause any changes, especially when the real change on the horizon was only something very rich companies could invest in.
SBC also bought, Pacific Bell, Ameritech and AT&T, when it did, it changes its name to AT&T. Later they bought out BellSouth, and changed its name as well. Cingular grew in phases as they acquired former RBOC's, but once SBC bought out BellSouth, Cingular became AT&T Wireless.
The current corporate entity that calls itself AT&T is formerly SBC.