Adamantine metal was known as "adamantite" in earlier D&D products.
In AD&D 1e, Gygax refers to the metal as "adamantite". Later writers, during AD&D 2e, would correct this nomenclature, since the English suffix -ite normally denotes a mineral, and the metal was renamed to adamantine.
Drow of the Underdark (1991) retconned that "adamantite" was a mineral from which the metal alloy adamantine could be made (credit to illustro's answer for this, which deserves upvotes). Pure adamantite worked into a metal is called "adamantium", which Volo's Guide to All Things Magical (1996), p.55, carefully renames to "adamant", defining adamatine as a durable alloy of adamant, silver and electrum.
However, this is subsequently contradicted by the D&D 3.5 Dungeon Master's Guide (2000), p. 283, where adamantine is simply a unique meteoric metal. Magic of Faerûn (2001) concurred with this and wrote off the "alloy of silver and electrum" theory described in Volo's Guide as a fanciful myth.
The connection between "adamantite" and the drow is that this was the nomenclature used by Gygax when he wrote D3 Vault of the Drow (1978). Even in the specific context of the drow, we see this corrected to "adamantine" in later books (e.g. Drow of the Underdark (2007) p.199). From 3e onward, the older term "adamantite" was almost never used.
Adamantite
"Adamantite" appears briefly in the AD&D 1e Player's Handbook (1978), and again in the Dungeon Masters Guide (1979), where it is a material certain items are made from: Daern's Instant Fortress (p. 152) has "adamantite walls", The Saw of Mighty Cutting (p. 153) is an "adamantite blade", and the Talisman of the Sphere (p. 155) is an "adamantite loop". +5 armor is adamantite alloyed steel (p. 154).
An "adamantite door" appears in Gygax's S1 Tomb of Horrors. Even after Gygax's departure fron TSR, the use of "adamantite" continued into many products of AD&D 2e, such as the Planescape Planes of Conflict (1995), where adamantite dragons are said to inhabit Bytopia (Liber Benevolentiae, p.43).
Adamantine
Some AD&D 2e books referred to "adamantine". After Drow of the Underdark (1991), Book of Artifacts (1993) refers to the metal "adamantine" (credit to illustro for this reference).
However, the use of "adamantine" to refer to the metal was standardized with D&D 3e (2000), where it appeared in the Dungeon Master's Guide, and has remained so ever since. References to "adamantite", "adamantium" and "adamant" have been discontinued.
D&D 3e routinely converts specific instances of "adamantite" to adamantine. Daern's Instant Fortress is now made of adamantine. Bytopia is now inhabited by adamantine dragons (Dragon #321, p.44). The 3e Tomb of Horrors web conversion even describes the 1e-era doors as having been made of adamantine (p.25):
The 1-foot-thick steel door (it's too expensive for the demons to keep replacing adamantine doors) is suffused with a globe of invulnerability effect.
Drow connection to "adamantite"
D3 Vault of the Drow described the drow working an alloy of "adamantite" and steel, which they draw into a wire used to make a fine mesh for armor. (p. 13):
These creatures dwell in a pool of molten lava at the far end of their smithy, and they make the adamantite alloy and draw the wire.
And:
Drow wear a fine mesh armor of exquisite workmanship. It is an alloy of steel containing adamantite [...]
The value of this alloy is that when it is exposed to the strange radiation in the Drow homeland (see MODULE D3, VAULT OF THE DROW) for a period of one month, its magical bonuses come to the fore.
I cannot find any reference to adamantite working differently with poison, except that both drow adamantite armor and drow poison lose their efficacy when taken from the Underdark to the sunlit surface.
In fact, the drow specifically have to re-apply their poison over time:
Drow sleep poison decays instantly in sunlight. Its power is lost after about 60 days in any event, and the coating on the small bolts and javelins must be periodically renewed with fresh applications of the fungoid substance. The Dark Elves will often have small barrels filled with several packets of this poison, each sealed to insure the poisonous substance remains fresh for about 1 year.