I don't see why both can't happen. They surely can use tech from Sonar in BandLab since they now own it. For instance a BandLab Pro Channel? But they can also both remain distinct and separate products. Maybe one day it will be a "BandLab powered by Sonar" type of thing ... not that they would ever name it as such.
I did a little more experimenting last night and still experienced some weirdness working with the tools in BandLab. But at least now I can sort of see what is going on. First off, I was definitely using Chrome as my browser. But when I tried to record live MIDI using my Focusrite Scarlett 18i20 and my M-Audio controller, it records as if the sustain pedal is constantly engaged. Yesterday I described it (above) as "overlapping notes", but I can see now what is going on. Anytime I load a synth into a track and hit record all my MIDI notes are stacked up and all play constantly. They just keep building up and never disengage until I hit mute or delete the track.
I'm still trying to determine if there is a simple fix for this on my end or if this is just how it's going to be for me on BandLab with my current equipment. If so, I can employ some of these workarounds we have been discussing like bringing in tracks from Sonar.