Rumor and rumour are the same word with the same meaning; rumor is the American spelling and rumour is the British spelling. If you are writing for a British or Commonwealth audience, keep the u. There is no difference in meaning, pronunciation, or grammar between them.
The core difference
Rumor and rumour are identical in meaning; the only difference is American versus British spelling.
- rumor — American spelling: A rumor spread that the factory was closing.
- rumour — British spelling: There's a rumour going around the office about redundancies.
How to tell them apart
There is nothing to tell apart in meaning here, only in spelling convention. Both words trace back to the Latin rumor, meaning common talk or noise, and both can work as a noun or a verb, as in it was rumored that two companies were merging.
The mix-up usually shows up when a writer switches between American and British style guides mid-document, or copies text from a US source into a UK one. The fix is simple: pick one spelling convention for the whole piece and stick to it, the same way you would with color and colour.
