There is a separate term for a hand - "кисть руки". But it's not used in the colloquial speech. It sounds clinical and formal. "Рука" works well enough. Most of the time people have no problem getting the intended meaning from the context.
I'm not sure why but in Hebrew and informal Arabic (at least the dialect I know) it's the same. People would use the same word to refer to both and you'll know from the context (although there's a word for "arm")