When used as a command, there is no difference. But when used in other contexts, there is a difference. For example, "There was a long wait to get my lunch." But you would not say, "There was a long hold on to get my lunch." "Hold on" may also be used as an action such as holding on to something. "I need to hold on to this." or "He is holding on to that paper."

as eddie said, it can be represented differently in context but also wait and hold on represents a time interval. This means when the word 'wait' is used, the wait can represent anytime in general (one hour or one year) but hold on is generally used for short amount of time such as 'hold on a minute' or 'hold on a second'..........i hope it helps.......