It is difficult to systematize the D&D tradition because it is inconsistent, incomplete and highly conflictive. This is due to its ad hoc development and evolution. For example, initially the Grey Elf gains an Intelligence bonus, but the High Elf does not. This is true for 1e, 2e, and 3e. However, in 4e, the merger of High and Grey to become the Eladrin made the High Elf an Intelligence Elf, and this tradition continues into 5e, where the High Elf is an Intelligence Elf.
Probably, for most players here, the High Elf with an Intelligence bonus feels familiar. But the conflation of the High Elf with Intelligence is unfortunate. Charisma is the more appropriate trope for the Elf, and D&D 3e, 4e, and 5e fully supports the use of Charisma for magic. Indeed, Charisma especially associates with innate natural magic, which is also an Elf trope.
The origins are awkward. The first 1e book is the Monster Manual, mentioning five types of Elf (Untyped, Aquatic, Black, Gray, and Wood) − and makes no explicit mention of Dexterity, but does mention Intelligence for Gray and Strength for Wood. Later, comes the 1e Players Handbook, it specifies the untyped Elf is called the High Elf, the High Elf is the only playable type of Elf, and the High Elf has Dexterity +1 and Constitution +1. Only the High Elf. Later, the Unearthed Arcana makes other Elf types playable, and specifies the Drow can use the High Elf Dexterity and Constitution modifiers. But the Gray Elf, Wood Elf, and Wild Elf, remain ambiguous, and might not receive a Dexterity bonus. The point is, early D&D had various conflicting portrayals of the types of Elf, even things we take for granted today.
The existence of a Grey Elf that gains Intelligence but lacks Dexterity has enduring traction. In 2e for example, the Tulani, the Eladrin counterpart of the Grey Elf, is the most intelligent but also the strongest without a hint of Dexterity or frailty, albeit this Strength is explicitly superfluous because of the magic for combat. In 3e, the Forgotten Realms counterpart of the Grey Elf, namely the Sun Elf, receives a bonus to Intelligence and no bonus to Dexterity. In 4e, the Eladrin Gray Elf is Charisma +2 and Intelligence +2. Dexterity is absent for certain traditions about the Gray Elf.
The 1e Unearthed Arcana (including errata in a Dragon magazine) illuminates the Elf types. It subdivided the Charisma ability score into a mental component Charisma and a physical component Comeliness. Comeliness quantified physical beauty. Ultimately, this division caused more problems than it solved, and while enjoying a kind of puerile mirth, never gained serious traction in the D&D tradition. Of interest here is its characterization of the Elf types. The Comeliness correlates with the Charisma of each Elf type, in the sense of sensual presence, visual appeal, and artistic style.
D&D 1e
Gray Elf: +2 Comeliness
High Elf: +2 Comeliness
Half Elf: +1 Comeliness
Wood Elf: +1 Comeliness
Female Drow Elf: +1 Comeliness
Wild Elf: +0 Comeliness
Valley Elf: +0 Comeliness
Male Drow Elf: −1 Comeliness
Later editions of D&D will fetishize the beauty of the Drow Elf, eventually making it a definitively beautiful Charisma race. But in its original concept in 1e, it exhibits ordinary Charisma comparable to mundane humans. (Albeit the female dominance includes being slightly more appealing, and the male poorer.)
In any case, when recombining Charisma and Comeliness back into the single Charisma ability score, D&D 1e defines two types of Elf as quintessential Charisma races: Gray Elf and High Elf.
Note the noncharismatic Valley Elf versus the charismatic Gray Elf, even tho both enjoy a bonus to Intelligence. Note also, the 1e High Elf is Charisma +2 and Dexterity +1.
With all of these D&D traditions in mind, I want to see the D&D ‘standard’ Elf, namely the High Elf, being an innately magically Charisma race. In other words, a kind of Sun Elf.
Sun Elf
• Sun Elf: Cha +2, Int +1
• High Elf: Cha +2, Dex +1
• Aquatic Elf: Cha +2, Str +1
Moon Elf
• Wood Elf: Dex +2, Wis +1
• Wild Elf: Dex +2, Str +1
• Drow Elf: Dex +2, Cha +1
• Valley Elf: Dex +2, Int +1
To reuse Shakespeares color scheme for the types of Moon Elf: Perhaps the Wild Elf, described in 1e as ‘very fair’ complexion, is the White Elf, here a savage beast unlike the Shakespearean noble beauty. The Valley Elf is Gray complexioned, which can correlate with the imagery of the mithril metal, and Eldritch Knights in Elven Chain. The Wood Elf is Green complexioned, the color of trees. The Drow Elf is Black complexioned and dark-dwelling.