<tl;dr> The difference between rights and privileges is critically dependent on the context in which the words are employed. That said, there are some general guidelines and common exceptions that are discussed below.
There are two closely related definitions of the word right that are relevant here:
proper claims that justly accrue to everyone; ...
I generally agree with LawrenceC's answer, but there is a bit more to say.
Lean is one of many verbs in English which can be used as transitive or intransitive. The intransitive use refers to the object which is tilted (as LawrenceC says):
The ladder was leaning against the wall.
The transitive use is causitive:
I leaned the ladder against the wall....
"Put" means to place an object somewhere.
"Keep" means to store an object somewhere on a permanent or long term basis.
I put my bag on the desk so the inspector could check it.
I keep my bag in the closet when I am at home.
The first is temporary. The second is more or less permanent. You can use 'put" for long term placements, but you cannot use "...