Oh that’s a good point you have there and app is just an abbreviation of Application which I think philosophically was a subset of Programs / Programmes.
It's always Program; in British English Program and Programme are not interchangeable and mean something quite different. A Program is a piece of computer software, a Programme is a series of planned events or a sheet of paper/booklet listing a series of details about an events. That we use the two distinctly is pretty powerful and the ambiguity of using one spelling is removed.
