That’s a good explanation of the difference.
Roots are just engrained because we used to be able to go get a worn roots blower from any diesel junkyard for a half days labor. Rebuild it with upgraded bearings and a couple custom plates and BLAMO! A blower has now become a supercharger. So tons of guys everywhere could diy big power affordably (kind of).
Twin screws are purpose built and didn’t come along till long after. Never seen a twin screw in a junkyard. More power but more money.
The last decade has seen a change in the production cost lowering on twin screws and no more dirt cheap supply of junkyard blowers. When they are there, the price is high.
If buying new- definitely twin screw if you can afford it.
The 6.5 supercharger- Roots design. Why? Cost. You could have a twin screw built for it, but would be cheaper to bolt in L5P.