-vigorous or not easily influenced, as a person; unyielding; stubborn: a tough man to work for.
-capable of great endurance
Strong means :
-having, showing, or able to exert great bodily or muscular power; physically vigorous or robust: a strong boy.
-aggressive; willful: a strong personality.
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source: tough - Definitions from Dictionary.com
strong - Definitions from Dictionary.com