I looked up the free dictionary, under symmetric it said another word for symmetrical. But which one is more common? Any other possible distinctions?
Here's one possible distinction I can think of.
symmetric applies in particular to relations: A is to B as B is to A, A does C to B and B does C to A, and so on. There is some kind of symmetric relation between A and B.
symmetrical applies in particular to objects: a circle is symmetrical radially, that's a symmetrical vase.
(Note: possible distinction. This does not mean that you cannot use either here - you can.)
Well, that's what occurs to me. However, this ngram suggests that the first bullet is no longer so relevant as it once was.
This ngram does support the second bullet somewhat.
No much difference. WordWebOnline suggests 'symmetrical' as a synonym or a variant of 'symmetric'.
symmetric - Having similarity in size, shape, and relative position of corresponding parts