They are indeed the standard symbols for those planets, and they do also coincide with the gender symbols, presumably because of the way the associations played out in classical mythology.
Fun extra fact: in Western alchemy, the symbols for major solar system objects ("planets", even though not all of them are planets by the modern astronomical definition) were also used to represent metals. Except HN seems to delete the symbols when I try to post them, so you'll have to look them up yourself, I guess!