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There are two Elos, for normal, one for both SR and TT, and one for Dominion.
There is a move/plan/thought about splitting TT normal Elo and SR Normal Elo. You'll forgive me not finding it in that mega-thread, but I read more or less all of Lyte's replies there and distinctly recall such being said.
Now, Elo is a bit wonky in smaller communities, so they may need to look into it. But no, it's the same system, and Dominion normal Elo is separate from TT+SR's. Back when lolnotes/lolmatches could retrieve Elo, we could pull the exact figure and see it for certain.
He is emphasizing classic, because he's emphasizing Ranked. And most people play SR ("Classic" being applied to SR shows you it's the one given the most attention). But almost anything said there is applicable to all of LoL, or all of Ranked.