'Take a rain check' means to put something off to another time. It was probably invented, and is most often used in America. 'Rain check' means to put something off until a nice day, when it's not raining. It's a wonder the British don't take lots of rain checks, the amount of rain we get!
In the USA, a receipt or the counterfoil of a ticket entitling you to see another baseball game if the original match for which the ticket was bought is rained off.