I don't see the difference as long as you are talking about lifting an object physically higher from the floor or ground. But 'hold up' can have the meaning of robbing or robbery. "I'll hold up the first person who comes out of the bank!" a robber might say. Or, "This is a hold up!"

Garters hold up stockings (hose).

Get That Clear - Hold Up - was created in 2007.

Hold Me Up was created on 1990-10-16.

S can hold no more than 2

P can hold up to 6

D can hold up to 10

F can hold up to 14