It is because they have different content as they are essentially different services.
The international version is co-owned by I.T.V. and the B.B.C. and provides access to current programmes from their channels as well as archive and original content. But current programming is not available on the British version because, obviously, it is freely available on television as well as the broadcaster's own free streaming services.
So Britbox U.K. is only archive content plus their few originals, is also now wholly owned by I.T.V., and from next month will be merged into their new streaming service anyway.
My question wasn't really about how they are different but rather what, if anything, changed to justify the notable price increase (especially in £) when the UK price stayed the same and the U.S. dollar is much stronger this year.
A year ago, the U.S. pre-sales tax monthly subscription price was $6.99 or about £5.10 which seemed to make senase as it was nearly the same as the UK pre-VAT monthly subscription price of £4.99. This year, however, the U.S. pre-sales tax monthly subscription price is $7.99 or about £7.10 which is significantly higher than the UK’s still £4.99 pre-VAT price.