So, are those two sites identical, or is the .com aimed more at a US audience?
An* international* audience.
The link here also explains why - because some video content is only licensed for UK audiences, and the international site carries advertising. The BBC is not allowed to incorporate advertising into its UK services (TV, online, radio or anywhere else - we pay a license fee instead).
You don’t so much get redirected to bbc.com, rather bbc.co.uk and bbc.com both resolve to the same internet address. It is up to the server how it decides to operate when it sees the different names. It seems that they simply treat them identically, but bbc.com in considered the primary name. The BBC site doesn’t just have local and international versions, it uses information about the browser’s address to tailor content on a country by country basis. Mostly this consists of pushing news items local to the viewer up the rankings. Similarly, UK local stuff gets pushed down.
.co.uk is from a different time - when the Internet was young. The UK uses different strings than the US, .co instead of .com, .ac instead of .edu, .mod instead of .mil. These were all established at much the same time, long before there was any default standard. (Here in Oz, I used to have an email address ending in .oz.au - where .oz was our .edu - however it has long since vanished.)