In the online version of Cambridge Dictionary, there are these definitions for the next two words:
Behaviour = the way that someone behaves
Behavior = a particular way of acting
What would be a difference between behavior and behaviour by some example?
They mean the same thing; behaviour is the British English spelling; behavior is the American spelling. The definitions say the same thing in different ways.
In fact, there is no difference between behaviour and behavior except spelling. The former is preferred in British and Commonwealth English, the latter is the American spelling.
The entries are confusing because there is no single "Cambridge Dictionary." Cambridge University Press actually publishes dozens of different dictionaries. Their website, however, searches them all at once, and returns definitions which may or may not be relevant to you.
When you look up behaviour, you are given entries from the Cambridge Advanced Learner's Dictionary & Thesaurus and the Cambridge Business English Dictionary. When you look up behavior, you are given the entry in the Cambridge Academic Content Dictionary, and from the Cambridge Business English Dictionary a pointer to the entry for behaviour. Because the target audience for each dictionary is different, you see slightly different entries, but this is a quirk of the Cambridge Academic Content Dictionary failing to synonymize the spellings.
I commend you for doing your best with references, but would also recommend you limit searches to a learner's dictionary (e.g. Collins, Oxford, Macmillan, Cambridge, or Merriam-Webster) to avoid this happening in the future.
In short, they're the same word spelt differently in the US and the UK.
It's not very obvious because of the way Cambridge has laid out their pages.
behaviour
noun UK US behavior
behavior
noun [ C/U ] CDN BR behaviour
behavior
noun [ U ]
→ behaviour
Wiktionary's entries are much clearer:
behaviour
Alternative forms
behavior (US)
behavior
Alternative forms
behaviour (UK)
Behaviour is the British spelling and behavior is the American variant.
The British spelling is in this case slightly more faithful to the etymology of the word.
The OED has the following etymology of behaviour:
- formed on the verb behave, by form-analogy with havour, havyoure, common 15–16th century forms of the word which was originally the noun aver (q.v.), aveyr, also in 15th century avoir; really Old French aveir, avoir, in sense of ‘having, possession,’ but naturally affiliated in English to the native verb have, and spelt haver, havour, haviour, etc. Hence, by analogy, have: havour, -iour: behave: behavour, -iour.
- The formation might be confirmed by the (apparently) parallel demeanour, from demean (oneself). For the -iour see havour.
The etymology of havour:
- Originally an adoption of the French aveir, avoir ‘having, possession, property, estate, wealth, etc.’, substantive use of avoir, Old French aveir ‘to have’.
- First used in English in the Norman form aveyr [...]; the Central French form avoir appeared about 1400, and displaced aver, except in the northern dialect, where that form survived in a specific sense.
- In 14–15th century, association with the English have, having, introduced the variants haver, havoir, havour, and the h was established before 1500. At the same time the parallel behavour was formed on the English behave; and in 16th century havour, beside its original sense of ‘possession’, took also that of behavour.
- Subsequently the termination of both words passed through -eour to -iour (cf. saviour, and vulgar ‘lovier’); the original sense ‘possession’ became obsolete; and, in the new sense, haviour came down alongside of behaviour, of which it may often have been viewed as a shortened by-form.
The American spelling, behavior, on the other hand, is effectively more 'phonetic' in nature, in that it dispenses with the u (there are only a few exceptions), which is otherwise not pronounced. At the beginning of the 19th century, Noah Webster pushed this change primarily via his dictionary, and Americans gradually adopted the new spelling. Etymonline.com says:
When the Americans began to consistently spell it one way, however, the British reflexively hardened their insistence on the other. "The American abolition of -our in such words as honour and favour has probably retarded rather than quickened English progress in the same direction." [Fowler]
If you're using American English, you should write behavior. If, on the other hand, you're using the British variant, write behaviour. The important thing is to be be consistent, as the commenters say: it'd be considered unusual to have both colour and behavior in the same sentence.
In short: pick a dialect and use it consistently.
