In the Fantastic Beasts and Where to Find Them textbook, we learn that wizards classify creatures as either "beasts" or "beings", where beings are usually defined by intelligence level:
Not until 1811 were definitions found that most of the magical community found acceptable. Grogan Stump, the newly appointed Minister for Magic, decreed that a “being” was “any creature that has sufficient intelligence to understand the laws of the magical community and to bear part of the responsibility in shaping those laws.” Troll representatives were questioned in the absence of goblins and judged not to understand anything that was being said to them; they were therefore classified as “beasts” despite their two-legged gait; merpeople were invited through translators to become “beings” for the first time; fairies, pixies, and gnomes, despite their humanoid appearance, were placed firmly in the “beast” category.
Fantastic Beasts and Where to Find Them: Introduction
And we see that trolls, for instance, are classified as beasts despite some rudimentary language skills:
The troll is a fearsome creature up to twelve feet tall and weighing over a tonne. Notable for its equally prodigious strength and stupidity, the troll is often violent and unpredictable. Trolls originated in Scandinavia but these days they may be found in Britain, Ireland, and other areas of northern Europe. Trolls generally converse in grunts that appear to constitute a crude language, though some have been known to understand and even to speak a few simple human words.
Fantastic Beasts and Where to Find Them: "Troll"
And "crudeness" is also a factor in being/beast classification:
Several highly intelligent creatures are classified as “beasts” because they are incapable of overcoming their own brutal natures. Acromantulas and Manticores are capable of intelligent speech but will attempt to devour any human that goes near them. The sphinx talks only in puzzles and riddles, and is violent when given the wrong answer.
Fantastic Beasts and Where to Find Them: Introduction
However, I don't see giants mentioned anywhere in the book, implying that they're perhaps classified as beings. (We even see centaurs and merpeople in the book, since they're classified as beasts by their own request.)
But trolls and giants... seem rather similar. We can see from Grawp that they're pretty violent and crude, even if they can understand / speak some rudimentary English:
“Anyway, Grawpy,” shouted Hagrid, looking up apprehensively in case of further falling eggs, “I’ve brought some friends ter meet yeh. Remember, I told yeh I might? Remember, when I said I might have ter go on a little trip an’ leave them ter look after yeh fer a bit? Remember that, Grawpy?”
But Grawp merely gave another low roar; it was hard to say whether he was listening to Hagrid or whether he even recognized the sounds Hagrid was making as speech. He had now seized the top of the pine tree and was pulling it toward him, evidently for the simple pleasure of seeing how far it would spring back when he let go.
“Now, Grawpy, don’ do that!” shouted Hagrid. “Tha’s how you ended up pullin’ up the others —”
Harry Potter and the Order of the Pheonix, chapter 30: "Grawp"
Given this, I'd be rather surprised if giants weren't classified as beasts... but I can't find any mention of them in Fantastic Beasts and Where to Find Them.
Do we know if Giants are classified as beasts or beings?