손대지 마십시오 Is a common phrase as well.
Does that mean "Dont touch me"? Or can it apply to anything? And is it literally "dont put your hand on it"?
Literally, 손대다 means to touch with one's hand. While it's often used in the same manner as 만지다, it is also used in a figurative sense. Its possible meanings include: to start (a work), to deal with, to lay a finger on (sexually or non-sexually), and to steal. 만지다 cannot mean any of them.