Less relatedly, I really hate when people use the eszett instead of a Greek beta. I just needed to get that out of my chest.
Out of curiosity I tried on my phone:
ß
Ss
SS
So my phone doesn't have that yet!
mine has it - ẞ
the small one is ß
Is the capital supposed to be shorter?
It's wider. Depends on your font and it's support though.
Oddly enough, yes (depending on font of course); compare "Sf": "ẞß" should have the same capital and lowercase-ascender heights, the latter of which is often higher.