Good to know! Hardcovers confuse me with stuff like this. That's one reason why I collect paperbacks instead.
I prefer paperbacks myself - mass market, anyway - cheap, fit in the hand, and, when they're science fiction, they just feel like real science fiction.
The dust jacket will 99% of the time indicate "Book Club Edition" which means it is NOT an actual first Trade edition. I only have a couple of BCE's in my collection... especially when the true firsts are very scarce and way out of my price range.
Yep, and SFBC books are usually (not always) smaller, clean-cut, and have clear and clearly glued signatures - other hardcovers will generally glue in a fake thing to make them look sewn if they aren't really sewn and can have uneven edges and so on. (SFBC books seem to lose their dust jackets a lot so you don't always have that to go on.

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I've been a member off and on for mumblety years and they are good for putting together omnibuses or original collections and for producing affordable editions of small press books. Straight-up book-to-book they're usually inferior editions to the hardcover and more expensive than the mmpb so, while I have a few of those, most of mine are from the other groups. But I don't pay any attention to first edition hardcovers other than to think "neat" when I have one.
Incidentally, you probably know this and I don't know if it makes any difference because SFBC books never seem to have much value but they are often the actual first editions in the sense that they beat the trade publisher by a month or three and, of course, in the case of paperback originals they're often the first hardcover whether they beat the paperback to press or not. But they don't seem to be considered "real" books.