Thought up another difference, this time with AND and &&:
'AND
IF BUTTON()AND #A THEN:?"Hello!"
'Press A and this message shows! Also works if you press another button while pressing A!
'&&
IF BUTTON()&& #A THEN:?"Hello!"
'Press any button and this message shows. #A is just boiled down to "well this one is true, hope the other one is also"