The variants in Play were around before there was a variant server. The latte is a completely different codebase and set of databases.
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Variants like Chess960 and Crazyhouse are playable in https://www.chess.com/variants, but they can also be played outside of that, for example in tournaments. The games in /variants seem to also be outdated in features, so I question their existence in the first place if you can play them outside of /variants anyway. Bughouse also redirects you out of /variants back to the regular site, but into the bughouse lobby, so why can't the others do the same?
Example:
https://www.chess.com/variants/crazyhouse/game/59473186
https://www.chess.com/game/live/96583038857
These are both Crazyhouse games, but the UI is different and you can only premove 1 move in the /variants version.
Also, why is my Crazyhouse rating in /variants 1598 when it's 987 outside of /variants?
Why are the queues separate? It doesn't make sense and it seems like this has been a problem for a long time. I hope Chess.com's staff fixes this.