I went back and forth a bunch on what the labels should be. Threshold to sensitivity was at the request of Mike Watt, that was the last change I made.
I'll admit I use those interchangeably, but to be accurate, an OTA is a type of VCA. VCA stands for Voltage Controlled Amplifier, but frankly most compressors can technically be considered voltage controlled amplification since the concept of compression is that the amount of amplification being done is adjusted based on the input of the circuit which is then converted to a control voltage. OTA, or operational transconductance amplifier, is a specific type of device that is used in compressors like the Dynacomp, Keeley, and Becos compressors.
With regards to the way the tube is used, I can clarify that a little further. The best parallel I can use is actually the Effectrode LA-1A. I'm using the tube in Single Slice in the same way they are in the LA-1A. The tube acts as an input stage to "flavor" the signal on the way in and also to feed the sidechain, which is the part that tells the compression engine (OTA in Single Slice, optical in LA-1A) how to adjust the signal output in relation to the input. There is then an additional tube stage that then further "flavors" and buffers the signal on the way out. So the tube isn't providing the compression per se, but it is very much involved in the way the output sounds as the response of the input stage can affect the reaction of the compression sidechain. We all know tubes sound different than their solid-state counterparts, but I think more important is the way they feel, and the reaction of a tube input translates through to the compression sidechain, so if I were to replace the tube stages in Single Slice with solid-state components, I would expect the compression to behave differently.
The only compressor type I'm aware of that works much differently that what I described above is a vari-mu compressor, which effectively changes the amplification factor of the tube. This is fairly complicated, uncommon, and expensive. I won't go into technical details on that right now because frankly I'm still trying to understand it myself.
A reasonably accurate summary, but as mentioned above the interaction of the tube stage and the compression sidechain behaves differently than it would a similar solid-state device, that's where the magic happens, in my opinion.
I hope this helps answer some questions, and I'm always around to answer more. I love questions because that's how you're supposed to get answers, you don't learn much without asking questions. So if there's any more out there please send them my way and if I don't have an answer already I'll do what I can to find it.