They have slightly different usage depeding on the context Кончай работу! sounds more emotional than Заканчивай работу but both are correct And one more thing - nowadays people avoid saying кончать because it means "to come" in sexual meaning

David, they mean the same. For some reason in literary langauge "закончить" и "окончить" substituted "кончить" . Maybe they sound more delicate:) "Заканчивать" is more commonly used in the sense "to finish doing something" and "оканчивать" is more commonly used in the sense "to graduate from" - but it is from "to finish [studies in] a school". "Оканчивать" can be used with noun (to finish a novel) but is not used with infinitives. But even with nouns, I think заканчивать is more common now. Сf. "окончание" - a final part of a story. When a novel is published in a magazine, the next part is introduced with "продолжение следует" ('continuation is following', to be continued) and the final part is introduced with "окончание следует". As it was pointed above, shorter "кончать" is more expressive.

Никакой разницы. Но слова =Кончить и кончать имеют также сексуальный смысл. В приличном обществе не употребляются

а еще есть "окончить" и "прикончить" ))

...one more meaning of the word кончать(кончаться) - to kill or to die Кончай его - Kill him Он уже кончается - He is dying