No, Windows NT until 4.0 had the same interface design as Windows 3.x (although there existed a semi-official SP/addon to give NT 3.5 the Chicago interface, making it quite similar to 95), and NT 4.0 came later than 95
Both OS lines were developed concurrently up until XP release where DOS-based 9x was abandoned and NT became the basis for every subsequent product. Plus of course there's that whole part of the story where MS teamed up with IBM and worked on OS/2.
NT got new 9x shell with 4.0 release but a beta package could be installed on 3.51 as well - tho, that could render some compatibility issues.
Actually I'd say Win2K was the merge point: its internal version is NT 5.0, while XP is NT 5.1 & 5.2. The Win2K UI is the first NT truly usable in a home situation, and last and best iteration of the Win95 UI before the plasti-color of XP. (Yes, that UI was last available as XP's "Classic Theme", but I'm giving it to 2K because XP doesn't really change anything.)
However Win2K wasn't really marketed to consumers as there were still some minor compatibility issues: particularly the DOS emulation was not great, so getting things like older games to work often required lots of tweaking to the launch process, and some things still might never work. Those compatibility settings got more options, saner defaults, and more automatic settings, in XP and later to go along with the full commitment of NT for everyone.
So, while DOS-based WinMe was actually released after Win2K, it was just a stop-gap to bring some more internet things, directx, and media player stuff, to home users while NT 5.x got it's compatibility and driver model in order. Except it was notoriously unstable, generally hated, and mostly forgotten.
