Is unable and not able are different words?

Yes, " Unable to " is very different to that of " Not able to ".

Grammatically any failure / fall of action is denoted by " Un+Able ". When people speak, they colloquially tend to get the " Not " as the strong notation of affirming the failure in action, deriving " Not able ". As a layman both means the same, but per grammar the fail of action is mentioned " Unable to ".

Regards,

Subu