I'm Canadian, and as far as I know they mean exactly the same thing...it is just a different spelling. In Canada, like the states, we say program. Programme is just the British spelling.
So you are correct in your example, although I would just use program in both cases. I am not sure if you should use the american and british version together in one sentence.
Maybe someone else knows the answer to that.
Sorry I couldn't help more.
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