Behavior is the preferred spelling in American English. Behaviour is preferred everywhere else. Other than the spelling, there is no difference between the two words. The spelling distinction extends to all derivatives, including behaviors—behaviours, behavioral—behavioural, and behaviorally—behaviourally.
Examples
For example, these American publications use behavior:
His behavior has cost him a seat in Congress. [Miami Herald]
When the frontal lobes are compromised, people become disinhibited, and startling behaviors can emerge. [The Atlantic]
The average behavioral differences between large samples of moms and dads are small, in statistical terms. [Wall Street Journal]
And these non-U.S. publications prefer behaviour:
Their crew was one of six boats that was punished by officials for bad behaviour during the 200-year-old competition. [Telegraph]
Road bullying is driver behaviour which intimidates other road users. [Sydney Morning Herald]
That’s a specific behavioural tick, and, what’s more, not a condition generally described as a nuisance. [National Post]
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