"hang on", is more of a informal way of saying "wait". They mean the same thing. People sometimes even say, "give me a second".

hang on is always used in phone call

"Hang on" and "wait" means the same as in telling someone to wait. But , "hang on" is more specific : it tells someone to wait FOR A WHILE until you are ready to talk to him about something -- on the phone or not. I need to talk to you . Sure , but hang on for a while coz Im on the phone

They both mean same thing, but as mentioned, " hang on " is used more on phone call. Like hang on a second, if the person gets distracted while on the phone.

'Hang on' is an informal way to say 'wait'. But it is not just that. 'Hang on' enters on the category of "Phrasal verbs" in English. These are a different kind of verbs. We don't have them in Spanish (as I see you speak Spanish). You can find more information here http://www.usingenglish.com/reference/phrasal-verbs/. Hope it helps!!!