Illithid tadpole is used when it may not be clear from context that mind flayer young are being described.
"Tadpole" seems to be the consistently used term.
From the AD&D 2nd Edition Monstrous Manual (pg. 251):
Mind flayers live about 125 years. They are warm-blooded amphibians, and spend the first 10 years of life as tadpoles, swimming in the elder-brain pool until they either die (which most do) or grow into adult illithids. On an irregular basis, adult illithids feed brains to the tadpoles, which do not molest the elder-brain. Illithids are hermaphroditic; each can produce one tadpole twice in its life.
From the 3.5e Monster Manual V, concerning the Madcrafters of Thoon, a race of creatures that was once Illithid (pg. 121-122):
Though the madcrafters of Thoon are no longer mind
flayers, they have a similar life cycle. The asexual madcrafters
give birth to thousands of tadpoles in a spawning pool deep
within the nautiloid vessel (not the same pool the Thoon elder
brain lives in). The tadpoles feast on each other in a frenzy
of cannibalism punctuated by long periods of group torpor. [...]
Like a traditional mind flayer elder brain, a Thoon elder brain
subsists on tadpolelike immature mind flayers.
Additionally, the 3.5e book Lords of Madness contains 45 occurrences of tadpole and its various forms. I won't reproduce all of them here.
From the 4e Monster Manual (pg. 189):
A mind flayer begins life as a small,
tentacled, tadpolelike parasite that invades the
skull of a helpless humanoid victim, devours its
brain, and then subverts the body to its own use.
In addition to the ceremorphosis mentioned in Volo's Guide to Monsters, we have a few more references in 5e material.
From the description of the Neothelid (VGtM, pg. 181):
On rare occasions, an illithid colony collapses, typically after an external assault, and the elder brain is killed. When that happens, the colony’s tadpoles are suddenly freed from their fate. They no longer serve as food, and in turn are no longer fed by their caretakers. Driven by hunger, they turn to devouring one another. Only one tadpole survives out of the thousands in the colony’s pool, and it emerges as a neothelid.
From Waterdeep: Dungeon of the Mad Mage:
Very rarely, an illithid tadpole transforms an individual into an ulitharid rather than an ordinary mind flayer.
From Waterdeep: Dragon Heist:
Qrr’zarq comes from a colony of mind flayers in Undermountain that wants to implant Xanathar with an illithid tadpole and, through a magical process called ceremorphosis, turn the beholder into a thrall. Qrr’zarq is waiting for an opportunity to implant the tadpole while Xanathar is alone and asleep.