In American English at least: If you were out walking with a friend and they were walking too fast. You could say "wait up" and "hold on" or "hold up". And they mean the same thing. Hold on is a little more versatile though. If you wanted some one to wait for an answer or to wait while you go and get someone or something they had requested, you would use 'Hold on" or "Hold on a minute" or "Hold on a second". The phrase is a bit casual so if you wanted to be more polite you would probably say, "Please wait for me." in the case of the first example or "Please wait right here, I'll let them know you're here." "Please give me a moment to respond to your question." Hope this helps

hold on intransitive verb a : to maintain a condition or position : persist b : to maintain a grasp on something : hang on wait up 1. Postpone going to bed in anticipation of someone or something, as in My parents always wait up until I get home, no matter how late it is. 2. Stop or pause so that another can catch up, as in Let's wait up for the stragglers, or Don't walk so fast; wait up for me. wait up (a minute) Wait for me while I catch up with you! Tom, who was following Mary down the street, said, "Wait up a minute! I need to talk to you." John: Hey, Sally! Wait up! Sally: What's happening? wait up (for someone or something) 1. Fig. to stay up late waiting for someone to arrive or something to happen. I'll be home late. Don't wait up for me. We waited up for the coming of the new year, and then we went to bed. 2. and hold up (for someone or something)Fig. to wait for someone or something to catch up. Hey! Don't go so fast. Wait up for me. Hold up! You're going too fast. See also: up, wait wait up (until something) to delay going to bed until a certain time or until something happens or someone arrives. Are you going to wait up until midnight? We waited up until we heard him come in the back door. See also: up, wait

As far as I know, 'Wait up' as an alternative for 'Hold on' is only used in US English. It would sound strange if someone in Britain were to say this. I could be wrong, but I believe that 'Hold on' is used by all English speakers, while 'Wait up' is used mainly by Americans. The standard meaning of 'wait up' is to wait for another person to come home before going to bed.