Is it okay to use hand soap to wash dishes?

I just came back to this area, and someone kept some of my stuff at their place while I was gone. Well, my dish soap was one of the things I stored there and it magically disappeared. (along with a towel, some body wash, a water bottle, a guitar capo, and about 700 Q-tips. Magic!) The hand soap didn’t vanish, so right now I’m using it to do dishes. What’s the difference between hand soap and dish soap, and is it okay to be cleaning with just hand soap if I’m dealing with things like raw meat?