The word programme has several meanings.
The one you’re certainly familiar with is something you watch on TV or listen to on the radio as in What’s your favourite TV programme?
It can mean plan or a series of actions as in
The ambitious reform programme developed by a group of independent politicians got no support from the government.
and
What’s the programme for tomorrow?
Another meaning is a leaflet that gives information about a play, concert etc.
She collects theatre programmes.
By contrast, program is a set of instructions given to a computer, i.e. All word processing programs these days have built-in grammar- and spelling-checkers.
There’s no such distinction in American English where one spelling program covers all of the above mentioned meanings.