The word women is used generally to represents all age of female human while ladies is used for specific purposes.
The word lady is still used as complementary word for example while calling and addressing like “excuse me lady” and “ladies and gentlemen” respectively while women word is not developed for the purpose of respect.
Lady is more polite word than women. That’s why for president’s wife, the words first lady is used to address.
There are distinction about games in Olympics both for ladies and girls.
For example ladies can take part in alpine skiing, cross country, figure skating, freestyle skiing, short track speed skating, ski jumping, snowboard and speed skating sports in Olympics. While there are limited sports are available for women in Olympics like biathlon, curling, ice hockey, luge and skeleton.