They have no difference in meaning, except word classes.
Definition of oppose by Merriam-Webster:
: to disagree with or disapprove of (something or someone)
: to compete against (someone) : to be an opponent of (someone)
: to try to stop or defeat (something)
Definition of opposed by Merriam-Webster:
: not agreeing with or approving of something or someone
: completely different
You can also try to google for the definition of opposed if you do not believe it has another form, which is adjective.
Hence, the first sentence was describing her opposition but the second sentence was trying to convey the message that John Kerry had opposed the idea.