Up to my knowledge, particles of phrasal verbs can be permuted (but if the object is a pronoun, it's obligatory: Put them on.(not put on them.)Originally Posted by hela
I think the object rarely affects the meaning. But you should know that the focus(of meaning) is on the final word. You could see the difference between them by making interrogations.
Question srelated to 'put on the coat' and 'put the coat on'
a. What did you put on?
I put on the coat.
b. How did you put the coat?
I put the coat on.