Putting it there is what happens the first time you carry it there and install it in its place.
Keeping it there is what happens over time. By keeping it there, you don't remove it after it is installed in its place.
In the context of those sentences, they both mean the same thing.
"put it there" means "put it there and keep it there".
"keep it there" means "put it there and keep it there".
Each of the verbs can be used to imply both.
CJ