It's a lie.
AT&T is trying to associate themselves with the "5G" industry moniker, but their network is really just 4G. They did the same thing with calling their 3G network a 4G network back 5+ years ago, and so then the phrase "LTE" became more common when some carriers launched actual 4G networks.
It's all just to confuse consumers and sell phone plans.
Generations absolutely matter and are way more than just bandwidth. The 4g vs 5g distinction carries hundreds of differences.
I think that that poster is saying is that unlike a lot of other technical indicators of Number + Letter, "3g" "4g" and "5g" don't have a specific technical definition, they're industry monikers for a host of various changes. Like, 10k means something -- 10 kilobits (10,000 bits); 1GB means something, it means 1 gigabyte; 1TB means 1 terabyte; 1080p means 1920x1080 with progressive scan; 11tfs is 11 teraflops if we're talking console "computing" power. Those are all technical specifications of something that are shortened down into something easy to say. "3g" "4g" etc are just generational monikers... The "third generation of wireless communication," or what have you, they don't have an intrinsic meaning outside of the industry nickname.
I think the 3G v 4G v 5G, etc., is more similar to the game that display manufacturers played 10-15 years ago with "ED" (Enhanced Definition), "HD" (High Definition), "TrueHD," "UHD", etc, TVs, where "HD" didn't really mean anything specifically... It could be 720p, it could be 720i, it could be 1080i, or 1080p... And it ended up becoming an industry buzz term that lost meaning from the technical specification. "HD" means something, like how "3G" or "4G" means something, but they're buzz words for a host of different technologies, not an actual technical specification, which is intentionally confusing to consumers.