Not much. It's just a question of spelling. American English always uses the spelling 'program'. In British English, there's a difference. We generally use the word 'program' to to refer to computer programs, and 'programme' to refer to all other meanings of the word ( a TV programme, a theatre programme, a programme of studies and so on).

As I remember it, the programme is the planification of events. At the theatre you receive a programme for the evening. Then there's a TV program or a computer program which take a different spelling.