Finalization of the issue

I have known that "live happily and live a happy life" mean the same for 10 years, and even though prepositional phrases function as an adjective or an adverbs, there is not much difference in meaning sometimes. However, they have turned out to be not true.

For example,

I bought some flowers for my mom.

I will throw a party for my girlfriend.

But I am really surprised and shocked that there is some difference in meaning and native English speakers usually think the prepositional phrases function as an adverb there and modify verbs.

And I have been thinking about it and I have come to a conclusion that if the prepositional phrases function as an adjective there, the meaning of the sentences is somewhat odd and there has to be some specific contexts in which there are more kinds of flowers or a party speakers want to distinguish from the others, but it is not common and true here.

So now I have gotten out of the long time confusion and I would like to make sure that there must be meaning difference or at least intention difference, when prepositional phrases function as an adverb or an an adjective?

Thank you as usual and I have learned a lot from you.