In which HP movie is something looking like an unicorn?
Are they really unicorns, or does it have another name ?
The first time we see mention of unicorns in the Harry Potter series is when Harry is looking at unicorn horns for sale:
Hagrid wouldn't let Harry buy a solid gold cauldron, either ("It says pewter on yer list"), but they got a nice set of scales for weighing potion ingredients and a collapsible brass telescope. Then they visited the Apothecary, which was fascinating enough to make up for its horrible smell, a mixture of bad eggs and rotted cabbages. Barrels of slimy stuff stood on the floor; jars of herbs, dried roots, and bright powders lined the walls; bundles of feathers, strings of fangs, and snarled claws hung from the ceiling. While Hagrid asked the man behind the counter for a supply of some basic potion ingredients for Harry, Harry himself examined silver unicorn horns at twenty-one Galleons each and minuscule, glittery-black beetle eyes (five Knuts a scoop).
Harry Potter and the Sorcerer/Philosopher's Stone, chapter 5: "Diagon Alley"
And then... spoiler for the first installment, since you don't seem to have read/watched it:
Harry has to go with Hagrid to find a hurt unicorn in the forest, which turns out to have been killed by Voldemort drinking its blood.
"Look there," said Hagrid, "see that stuff shinin' on the ground? Silvery stuff? That's unicorn blood. There's a unicorn in there bin hurt badly by summat. This is the second time in a week. I found one dead last Wednesday. We're gonna try an' find the poor thing. We might have ter put it out of its misery."
"And what if whatever hurt the unicorn finds us first?" said Malfoy, unable to keep the fear out of his voice.
Harry Potter and the Sorcerer/Philosopher's Stone, chapter 15: "The Forbidden Forest"
And since you're asking about the movie, here's a screenshot of the unicorn mentioned above from the first Harry Potter movie: