Which one is correct?
A: I set my bottle of water in the freezer.
B: I put my bottle of water in the freezer.
Is there any difference?
As has already been stated, both are correct and there is no significant difference between the two.
However, I might choose "set" over "put" in situations where I placed the object more carefully. If I have a bottle of water with a tight cap on it, I put it in the fridge. If I have a crystal bowl with a fancy trifle in it, I might set it in the fridge.
Both are grammatically correct. In fact the definition of 'set' includes the definition of 'put`. They are nearly synonyms in the usage in question.
I do agree with this comment that B ('put') is more common.
You should use the verb 'keep' for the things which you need to put in the fridge regularly.
Here neither 'set' or 'put' is correct.
You'll find the verb 'keep' printed on the medicine bottles and other things which are supposed to be kept in the fridge.
Definition of 'set' - to put someone or something in a position
'Set' is preferably used when you are allocating a place for a particular thing or you are setting a paritcular thing in a particular position.
So in your example it is less appropriate to use 'set' because you are not allocating a place to the bottle.
However 'put' should work fine here.