With regard to hypothetical species of the Elf creature type.
The names for some of the species can come from repurposing the names of 2e Celestial Eladrin. These names originate as something like "subraces" where each forms a rank of government (kinda racist), but here have nothing to do with ranks, and are simply names for separate species. Something like.
• Eladrin ‹ High, Ghaele
• Tulani ‹ Astral, Grey, Sun (Norsesque, radically magical, skyey)
• Shierre ‹ Wood
• Drow
• Grugach ‹ Wild, Bralani
• Nixie ‹ Sea, Noviere, Nereid
• Avariel
• Naiad ‹ Moon, Nymph
• Hamadryad
• Oread ‹ Fierre
• Banshee
There would be overlap between an Elf creature type and the Fey creature type. In Scottish lore an "elf" is a humansized fairy. In Norse lore "alfr" is a specific creature, but in British lore "aelf" came to apply to various creatures including Greek nymphs. The characteristics that caused an other creature to be understood as an "elf" are: human appearance, extreme beauty, supreme wielders of magic, foreseeing fate, luck. The Norse alfr is prominently male (the female is valkyrja/dis/norn), the Greek nymph is female (mostly?) and French feie are prominently female (but male is part of the society). Of course, in D&D the gender can be anything.
Possibly, have the Dwarf be a member of the Elf creature type.
Other creatures, including various sprites like Gnome, Pixie, Goblin, would be Fey. Fey is mainly a planar origin and encompasses everything from Hag to Centaur.
Especially when it comes to translating the D&D Elf traditions into separate species, they would need to be completely unlike each other.
(That said. I do think it is simpler to have one Elf entry, to represent every Elf that has ever existed in D&D, and let the player choose its spells. When worldbuilding, the DM can choose the spells that prevail in a particular Elf community.)