Why do turntables sound different?

They sound different for two reasons.

1/  The design choices of suspended, lightweight or mass and                implementation of materials choice and the drive method used.


                                                                                                               
2/  The use in the home environment from either proper, or poor set  up, in both basic parameters and adjustment ,and final placement.                                                                                                                                                                                                                                    

So far scientists among us don’t participate, and I suspect I know why - they have no idea.
If all seemingly great turntables sound different, than perhaps none of them sounds quite right. Each distorts and colors the sound in its own way.
I would also assume that mechanically matching table and arm could be important. And cartridge is the third element. Maybe all three should be matched ?

"Maybe all three should be matched"

I would add everything thing else in the chain.  One size fits all does not really fit in audio regardless of the ad copy and graphs.

Look at Michael Fremer's set-up in that small room with the Continuum TT and big Wilson speakers! I bet he's not too worried about vibrational interference, since the Continuum is a hefty beast indeed!

Actually, Mr. Fremer wisely gets quite nervous about vibrational interference. That's why he uses the super duper Minus K negative stiffness isolation stand for the Continuum. The new Obsidian version of the Continuum incorporates a lot of vibration isolation in its design, including magnetic levitation for the platter and a dedicated isolation system for the tonearm. The Continuum might be a hefty beast but the Earth is a heftier beast.