Your examples need a little change. You should qualify 'money' and say 'my money', 'some money' or similar. Saying 'money' by itself is not correct.
'Exchange' ALWAYS involves swapping something. "I'd like to exchange my Canadian dollars with US dollars". "I'd like to exchange my job with hers"
'Change' does not always involve swapping something. It can just mean making something different. "I'd like to change my job'. If you want to make it mean 'swap or trade' you need to use the word 'exchange' or add context (I'd like to change my job WITH hers).
In some situations as in swapping currencies, they are interchangeable, but 'exchange' is a more precise word to use.