They are the same; in fact, "cleaning" is better than "cleaning up." English speakers often add "up" to verbs, but it doesn't change anything in the meaning, so it has no purpose (e.g., "wake up," "heat up," "fix up," etc.). Of course, sometimes the "up" refers to direction and is appropriate (e.g., "I'm going up to see the boss on the top floor"); sometimes it is part of a phrasal verb (e.g., "catch up," "look up," "take up," etc.). However, it is often just an unnecessary addition, as in "clean up."