Is there a difference between 买 (mǎi), 购 (gòu), and 购买 (gòumǎi) which mean "to buy"?
买 is more casual. 

购 is formal when forming up with other characters: 购买，购票厅，购物，申购，团购，and etc.. These terms are formal both in written and spoken.

You can also consider 买 is short for 购买. 购买 is official term, so people just say 买... in our daily life instead of 购买. For example, 买菜，买车，买房子.

As this sign is posted in the Beijing airport, they should make it formal by 购票厅, instead of 买票厅.