Interesting that the perfective aspect is used here. I guess it's because the speaker wants the other person to finish waiting on them? Would the imperfective be okay as well? Or would it not have the same connotation?
"Жди меня" is going to carry with it a more prolonged sense of action. "Wait for me, I promise to come back (sometime)." It could also be used for a repetitive action: "Wait for me at this corner every day." If, however, you're running to catch up to someone, the waiting is a brief one-time event: "Wait, don't leave!"
When "подождать" is used in imperative it usually means that the object of waiting will definitely happen. And since it is perfective, it means that the waiting must be finished before another action can be started. So, "подожди меня" means "Wait for me, before starting doing something/going somewhere".
In some cases "жди меня" would work the same. In some cases it will not.