The verb "to hang up" can mean a few things. For instance, 1. to terminate/end a phone call -- He hung up the phone. = He ended the phone call. 2. to put something up in order to hang it -- I hung up my wash on the line. = I put my wash up on the line to hang it. 3. to keep held up, delayed, suspended, or stuck -- He pressed F5 repeatedly which just hung up the computer. = He kept pressing F5 which caused the computer to not respond anymore to input. The verb "to hang" has a number of meanings too. For instance, 1. to be or remain suspended -- The lights hung from the ceiling. = The lights were suspended from the ceiling. 2. to float as if suspended -- The smoke hung in the room. 3. to cause (something) to be suspended, as from a hook, hanger or the like -- I hung my clothing on the clothesline. / I hung a few photos on the wall. Sometimes they mean the same thing essentially; for instance, "I hung a few photos on the wall." = "I hung up a few photos on the wall.", especially if the photos are above eye level.

Hang: to suspend or be suspended from above with the lower part dangling free. Hang up: to put on a hook, hanger, etc. In this context, most of the time, "hang" and "hang up" are interchangeable. For example: "Please hang the pictures on the wall." "Please hang up the pictures on the wall." "You may hang your coat on the hook." "You may hang up your coat on the hook." However, in other contexts, they are not interchangeable. For example: "He was being rude over the phone, so I hung up on him." (you have to use the phrasal verb "hang up" here as we are talking about a phone call) "He is to be hanged for committing murder." (you have to use "hang" here because we're talking about the action of killing someone i.e. hanging him by the neck)