Kind of like AT&T TV, T-Vision aims to emulate traditional cable TV, but with the live channels delivered via streaming. But with T-Vision, the DVR does record the live streams to a local hard drive rather than using cloud DVR, like AT&T TV, where the recordings are stored out on a server. And you MUST use the T-Vision STBs. They don't let you access the service via an app, either in home or on mobile devices for out-of-home viewing.
T-Vision also differs from AT&T TV in that it's not really OTT (able to work over any broadband connection). T-Vision relies on having an agreement in place with local broadband providers to ride over their network connection for the last mile. So it's not even available for the vast majority of Americans. T-Vision exists in this weird no-man's-land between managed IPTV and OTT TV, between traditional cable and streaming.
The first-hand reviews I've read indicate that T-Vision (formerly known as Layer3 TV) is somewhat buggy. I think they've also been really slow to fulfill their promise in getting popular apps like Netflix rolled out to their set-top box. Unlike AT&T TV, which has access to the Google Play app store for thousands of Android TV apps, T-Vision has to get app developers to create apps just for them.
In all sorts of ways, T-Vision is less flexible than AT&T TV. I don't see it ever taking off. I think T-Mobile bought it mainly to acquire their talent, engineering, and existing channel contracts, to serve as the basis on which they could build a more future-proof app-based OTT TV service for delivery to smartphones as well as TV-connected streaming devices (much like AT&T TV/AT&T TV Now). My guess, though, is that T-Mobile will realize that it's going to be such an uphill battle to create a profitable pay TV service, given that they don't own any content (like AT&T, Comcast, Disney, etc. all do), that they'll just throw in the towel and decide to partner up with someone else.
That's what Verizon did. They did extensive beta-testing on a next-gen IPTV service that was going to replace FiOS TV, and perhaps also be distributed over Verizon's mobile service too. But the industry -- in terms of the economics as well as the technology-- was changing so rapidly out of their favor that they just chucked that new IPTV service. Instead, they've teamed up with Google to re-sell YouTube TV to their home broadband and mobile customer base. I expect we'll see T-Mobile do the same. Maybe they switch from "Netflix On Us" to giving all T-Mobile home and mobile customers the $13 bundle of Hulu, Disney+ and ESPN+ for free. And if they want cable TV, they can add on the Live tier to Hulu. They could even do like Verizon and AT&T and roll out their own little customized Android TV device that they give away to customers for free, except this one would be customized to feature Hulu.