This is an ancient technique. The Tale of Genji, written in the 11th century by Shikibu Murasaki and called by many the first full novel ever written, talks frequently about homage related topics. When a person would compose a poem, they would deliberately craft the words and phrasing to call in mind another famous poem. It was almost a requirement in some situations.
So an example, assuming you know the Star Wars series, would be writing a poem that said
Like a Jedi light saber
wielded by a spinning green master
your anger slashed through my heart
leaving me bewildered
How is this different than plagiarism? Plagiarism is, by definition (read link above) a deliberate stealing of a person's phrasing. No idea can be copyrighted. There cannot be only one story about boy wizards. Any person can write about boy wizards. Any person can write about brave princesses and evil generals. However, if in your story you have:
Princess Zeia: Governor Tarkin, I should have expected to find you holding Vader's leash. I recognized your foul stench when I was brought on board.
Governor Zarkin: Charming to the last. You don't know how hard I found it, signing the order to terminate your life.
Princess Zeia: I'm surprised that you had the courage to take the responsibility yourself.
Governor Zarkin: Princess Leia, before your execution, you will join me at a ceremony that will make this battle station operational. No star system will dare oppose the Emperor now.
Princess Zeia: The more you tighten your grip, Tarkin, the more star systems will slip through your fingers.
That is now plagiarism. You can have the same *feelings*. You can't have the same dialogue and exact plot line, though.
What would be homage, then? Let's say a certain director has a technique of having "flying doves" at climactic moments in his movie, to symbolize freedom and longing. Then let's say another movie is filmed about a similar theme, and at the right moment there are a bunch of flying doves. The second director is not plagiarizing the first director. You can't copyright flying doves :). The second director is deliberately wanting people to think of the first director in that situation, a tip of the hat in essence to say "I give credit to this previous master for inspiring me." It's meant as a flattering kudos.
Of course, a homage only really works if the audience knows of the first author's work and gets the connection! So a homage needs to be both known and appropriate to work well.
The main key here is that the homage is a highlight in an original story.
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