I'm pretty sure cs has no lvl requirement. The stash in FH doesn't have the lv4 requirement btw. Strange, but true :)
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Yes, you'll see both wordings in the UI when you're in the store. Conveniently, CS is an abbreviation for both.
If you have an iPad, you'll also see "Auction Haus" in addition to "Consignment Store" and "Consignment Shoppe".
A foolish consistency is the hobgoblin of little minds
—Emerson