In HP and the Order of the Phoenix, we see this magic occurring;
What's this called?
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It may not be Apparition. Apparition in the books basically involves appearing out of thin air with a loud noise
“They don’t need the car!” said Ron impatiently. “They know how to Apparate! You know, just vanish and reappear at home! They only bother with Floo powder and the car because we’re all underage and we’re not allowed to Apparate yet...”
Harry Potter and the Chamber of Secrets, Chapter 5, The Whomping Willow
Books don't talk about leaving a trail of smoke behind like shown in Order of the Phoenix and other movies.
Harry Potter wiki is not really reliable since it lacks citation. But it has following text:
Death Eaters are shown physically collapsing into thick black plumes of smoke, shooting off into the sky, and being able to go wherever they want to, while doing this. Even though many people think this is apparition, it is not. It is just an ability that was given to the Death Eaters in the movie series.
But on the contrary Fred and George Weasley Apparate normally (as mentioned in the book) in Order of the Phoenix film
Fred and George Weasley, near the beginning of the Order of the Phoenix film, show Apparition as it is shown in the books, by merely appearing out of thin air with a loud noise, usually startling the people around them like Molly Weasley
Even the wikipedia page for Magic in Harry Potter has something similar
In the Order of the Phoenix film, Death Eaters and Order members Apparate and Disapparate in clouds of smoke. Death Eaters appear and disappear in black smoke, Order members in white. In the film, both sides also appear to be able to "half-apparate" in which their bodies were made out of smoke, giving them the ability to fly. This is not canon to the books and probably just used for more cinematic, atmospheric purposes. Interestingly, both times Fred and George apparated and disapparated, they did it with a pop as in the books.
Referring Magic in Harry Potter
I believe it is a different spell added for cinematic effects. There are no canons available for this spell.
In the books Voldemort and Snape can fly this way as collapsing into thick columns of black smoke and flying but in the movies it is an ability given to the death eaters for the dramatic exterior of apperation. Members of the order of the phoenix are seen collapsing into thick pillars of white smoke and flying just as death eaters so this proves that unsupported flight was duplicated. Only for the movies can this be apperation. But for the books it is Voldamort and Snape's invention of unsupported flight.