Call of Cthulhu/Great Old Ones vs Outer Gods
Classification
"Very few people dispute that Azathoth and Yog-Sothoth are Outer Gods instead of Great Old Ones, although some accounts make them ancestors of a few Great Old Ones. This has led to the theory that "Great Old One" is the term for everything younger than Cthulhu and Tsaggothua, and "Other God" or "Outer God" to be everything older."
ref [1]
--
Great Old Ones vs Great Ones vs Outer Gods vs Elder Gods
Great Old Ones: "An ongoing theme in Lovecraft's work is the complete irrelevance of mankind in the face of the cosmic horrors that exist in the universe, with Lovecraft constantly referring to the "Great Old Ones": a loose pantheon of ancient, powerful deities from space who once ruled the Earth and who have since fallen into a deathlike sleep."
The Great Ones: are the "weak gods of earth" that reign in the Dreamlands. They are protected by Nyarlathotep.
Other "Outer" Gods: As it is known in the Mythos, the Outer Gods are ruled by Azathoth, the "Blind Idiot God", who holds court at the center of infinity.
Elder Gods: In post-Lovecraft stories, the Elder Gods oppose the likes of Cthulhu and his ilk. Derleth attempted to retroactively group the benevolent deity Nodens in this category (who acts as deus ex machina for the protagonists.
ref: [2]