I know of no difference in meaning. That said, I find رجع is much more colloquial, and عاد much more standard.

Sorry I was wrong ! I made new research and found that رجع is used with motion "to go back" but عاد is used with actions in Quran we have ارجع الى ربك فسئله .... حتى يرجع الينا موسى this is in the meaning "to go back" but when to "re do" is ment we have لا تعودوا لمثله ابدا وان عدتم عدنا ====== this is in the standard Arabic of Quran but in the modren Arabic people mix that and never care or know the difference even me before this night !!

both are the same meaninig but رجع is used in Colloquial and عاد is used in classical arabic and they mean :get back

These words have the same meaning in Arabic, and in Arabic we have a lot of Synonyms which do the same meaning, So, عاد=رجع and sure both are in the past.

it is similar to roof and ceiling !! when you are in the point A and someone went to point B then back to you you will say he has returned عاد but if you were in point B and that person left you and back to his first A point you will see رجع