点单 and 点菜 both mean 'to order', but 点菜 specifically refers to ordering dishes at a restaurant, while 点单 is broader, also used for tea shops, cafes, and any QR-code ordering system. 点单 has become very common with mobile-app ordering.
culture
Most casual restaurants in mainland China now use 扫码点单 (scan-to-order): each table has a QR code, you scan with WeChat, browse the menu, pay, and your order goes straight to the kitchen, no waiter needed.
