I started out as a strat-player, and I did a lot of gigs with the trem blocked (mainly so that we could keep playing in a 3-piece when I broke a string).
Later I started using guitars with shorter scale lengths as well. I found these felt a lot floppier, so I had to up the string gauge for the shorter guitars.
I settled on using my standard (at the time) 10s on Fender scale-length and 11s on Gibson. They felt reasonably close, and I did that for a few years very happily.
Then I "retired" and didn't touch a guitar for years.
When I "started up again" as a home player/recorder, I was playing a strat and broke a string. I didn't have any 10s, so I put 11s on as a temporary measure. I absolutely loved it. I decided to live with 11s on everything. You get used to it quite quickly. I find I can switch scale lengths, tensions, fretboard radius, neck profile, fret size/profile, humbuckers to singles, etc, etc, etc, really quickly nowadays. It wasn't always like this - it used to take me ages to acclimatise myself, I'd be worrying I was playing badly, etc. I decided to stop (like Slarti) trying to make them feel the same - I just embrace the differences, and I seem to be able to put one down and pick another up and still sound the same, I just feel a bit different and maybe play a bit different.
Anyway, here's why scale length affects the tension: with a longer scale length but the same weight of string, you need to increase the tension to get it to the same pitch - so a longer scale feels "tougher" and less "giving" when using the same strings. That's all it is.
Now, whether a floating trem affects tension - I personally think it does, it feels like it to me... but I've heard arguments it doesn't and that we just imagine it.
There's another thing I find affects tension on guitars with separate bridge and tailpiece - try raising and lowering the tailpiece. Screw it down and (I believe) you get stiffer strings for the same pitch. That's what I find on my gibson guitars. I no longer try to get the tailpiece down to the body "for the tone" - I set it for the feel of the strings.