The difference is so small that people don't give too much care about which should be used. Also the use of each word is defined by been formal or informal (in some places)
- Acordar -> Agreement between two or more parts.
- Acordar -> Used instead of recordar / "no me puedo acordar donde puse
There is also a new variant to these two used in some places
- Re-acordar -> Start to remember something again.
If used on the sense of "remembering" like in ¿oye, te acuerdas de esa película?, The question implies that both persons where together watching the movie, while ¿oye, recuerdas esa película? the person could had seen the movie at a different time (not with the person that ask the question). Although This is not a rule, and may not be correct in all countries.
Without been an expert I will say that personally, I will use one instead on the other depending on the case (formal or informal).
To answer your question correctly I will say that the use depends quite a lot on the region/country and unfortunately there in no rule that can be successfully applied to all countries (since the use of the word or meaning given in some countries may differ from the sense or meaning of the word given by others in other countries).