The first video being perceived as smoother is mostly because of motion blur, yes. In some instances (honestly way too many in my experience) the "quality" of the demo can also be a factor. By that I mean, sometimes if your connection is a bit iffy your POV demos might look kinda shit and stuttery, and if the server you were playing on hasn't been restarted in a while or anything like that the STV demos might be kinda shit and stuttery. Those you can't help too much from my experience.The best I've been able to do to minimize it is to set your interp to 0.1 and set cl_smooth to 1 when watching demos. Change it back before you actually play though if it isn't already in your autoexec.
In the first video you linked, if you go to 1:14 you can see that snakewater demo looks buttery, and the process clip right after looks pretty stuttery. Sometimes it be like that.
If you want to be a true chad and go whole hog, I'm 99% sure there's a way to convert STV demos into SFM scenes and record from there, but I haven't looked into that too much because I absolutely cannot be fucked.
Also on motion blur really quick: I stan motion blur in frag videos if done right, because it really can make your shit look clean. Using the in-game motion blur is a hard no for me though, and if I ever add any motion blur I do it in post with RSMB in After Effects. It's kind of a pain, but at the very least this might be able to help alleviate the fuckign dog shit inconsistent demo experience in this god forsaken piece of shit fucking game.