There is a difference between the books and the films.
In the films the
Uruk-hai are attributed to
Saruman out of some sort of weird slime pods.
In the books, Saruman seems to have bred half-orcs (in two varieties), while the Uruk-hai (great soldier-orcs) are from
Mordor initially.
Here is an essay:
The Uruk-hai are first bred by
Sauron, not Saruman, and Uruk-hai are not Half-orcs.
Uruk-hai means Orc-folk (
uruk=
orc, hai=folk) (PE 17, Words, Phrases and Passages in LotR):
"B Urukhai Uruk-hai 'Orc-folk'"
and:
"'The
Black Speech was not intentionally modeled on any style, but was meant to be self-consistent, very different from
Elvish, yet organized and expressive, as would be expected of a device of Sauron before his complete corruption. It was evidently an agglutinative language, and the verbal system must have included pronominal suffixes expressing the object, as well as those indicating the subject: -ul is a pl. objective, translated 'them', and -ûk an element meaning 'the whole, all' (thrakatalûk I 267 is a misprint for -ulûk, as correctly written in the flame letters). The stem burz 'dark' is also found in the later Lugbûrz =
Barad-dûr; in the archaic
ring-inscription burzumishi is evidently made up of this stem + a particularizing suffix or 'article' um, and an enclitic 'preposition' ishi 'in, inside'. The debased form of the B. S. which survived in
the Third Age only in the
Dark Tower is seen in a few names (as Uruk-hai 'Orc-folk') and the fragment of vituperation uttered by one of
Grishnakh's companions, emissaries from Sauron. I have tried to play fair linguistically, and it is meant to have a meaning and not to be a mere casual group of nasty noises, though an accurate translation would even nowadays only be printable in the higher and artistically more advanced forms of literature. According to my taste such things are best left to
Orcs, ancient and modern."
Uruks is an Anglicization of Uruk-hai (UT, Index):
"Uruks Anglicized form of Uruk-hai of the Black Speech; a
race of Orcs of great size and strength."
Late in the Third Age the term Uruk-hai refers to the great soldier-orcs that came from both Mordor and
Isengard (LotR, App. F):
"Orcs and the Black Speech. Orc is the form of the name that
other races had for this foul people as it was in the language of
Rohan. In
Sindarin it was orch. Related, no doubt, was the word uruk of the Black Speech, though this was applied as a rule only to the great soldier-orcs that at this time issued from Mordor and Isengard. The lesser kinds were called, especially by the Uruk-hai,
snaga ‘slave’."
Uruks first appeared in the 2400's of the Third Age (App. A):
"In the last years of
Denethor I the race of uruks, black orcs of great strength, first appeared out of Mordor, and in 2475 they swept across
Ithilien and took
Osgiliath."
Saruman only started using them late in the Third Age (App. A):
"In 2989 Théodwyn married Éomund of Eastfold, the chief Marshal of
the Mark. Her son
Éomer was born in 2991, and her daughter
Éowyn in 2995. At that time Sauron had arisen again, and the shadow of Mordor reached out to Rohan. Orcs began to raid in the eastern
regions and slay or steal
horses. Others also came down from the
Misty Mountains, many being great uruks in the service of Saruman, though it was long before that was suspected."
Uruk-hai were involved in the revolt at
Cirith Ungol (LotR, Land of Shadow):
"‘Whose blame’s that?’ said the soldier. ‘Not mine. That comes from Higher Up. First they say it’s a great
Elf in bright armour, then it’s a sort of small dwarf-man, then it must be a pack of rebel Uruk-hai; or maybe it’s all the lot together.’"
The Uruk-hai (as great soldier-orcs) are not exclusive to Saruman, nor bred (at least initially) by him. They are Sauron's doing.
They also are not the 'half-orcs' which Saruman did breed (
Morgoth's Ring, Myths Transformed, Orcs):
"Finally, there is a cogent point, though horrible to relate. It became clear in time that undoubted
Men could under the domination of Morgoth or his agents in a few generations be reduced almost to the Orc-level of mind and habits; and then they would or could be made to mate with Orcs, producing new breeds, often larger and more cunning. There is no doubt that long afterwards, in the Third Age, Saruman rediscovered this, or learned of it in lore, and in his lust for mastery committed this, his wickedest deed: the interbreeding of Orcs and Men, producing both Men-orcs large and cunning, and Orc-men treacherous and vile."
Further the "half-orcs" are distinguished from the Uruks in both LotR (Flotsam and Jetsam):
"He emptied Isengard. I saw the enemy go: endless lines of marching Orcs; and troops of them mounted on great
wolves. And there were battalions of Men, too. Many of them carried torches, and in the flare I could see their faces. Most of them were ordinary men, rather tall and dark-haired, and grim but not particularly evil-looking. But there were some others that were horrible: man-high, but with goblin-faces, sallow, leering, squint-eyed. Do you know, they reminded me at once of that Southerner at
Bree; only he was not so obviously orc-like as most of these were.’
‘I thought of him too,’ said
Aragorn. ‘We had many of these half-orcs to deal with at
Helm’s Deep. It seems plain now that that Southerner was a spy of Saruman’s..."
...and in UT (
Battles of the Fords of Isen):
"This was barely done when disaster came. Saruman’s eastern force came down with unexpected speed; it was much smaller than the western force, but more dangerous. In its van were some Dunlending horsemen and a great pack of the dreadful
Orcish wolfriders, feared by horses. Behind them came two battalions of the fierce Uruks, heavily armed but trained to move at great speed for many miles. The horsemen and wolfriders fell on the horse-herds and picketed horses and slew or dispersed them."
...and later:
"As soon as the enemy had gained possession of the eastern end of the Fords there appeared a company of men or orcmen (evidently dispatched for the purpose), ferocious, mail-clad, and armed with
axes."