1. She put a blanket over the sleeping baby.

2. She put a blanket on teh sleeping baby.

(Can we use both over and on? What is the difference between them?)

2 answers

Yes, you can use both. #2 is a bit more vague, perhaps. Sometimes babies are wrapped in blankets, as in being dressed in a blanket, or having it "on" as in having your pants and shirt on. But, both do mean the same, really.
1. She put a blanket over the sleeping baby.

2. She put a blanket on the sleeping baby.