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If you can get all the same suit in your hand, you're probably not far from being able to check for riichi anyway though.
https://steamcommunity.com/sharedfiles/filedetails/?id=1510481394
Accordingly, a half flush is all of one suit + any combination of honor tiles.
What is similar is a Full Straight, which is 123, 456, 789 in one suit in your hand, but all the other tiles in your hand can be anything else. The Full Straight and Full Flush can be in one hand if you're amazingly lucky.
EDIT: I might have misinterpreted the question. By 'sets' I thought you might have been referring to sequences like 123, as opposed to triplets or quads, which all count as one meld; while you're using set to refer to melds I believe? I'm perhaps too into mahjong now I'm getting flustered by semantics.