The name Corten (also written Cor-ten) is trademarked to US Steel, the inventors of the alloy. US Steel sold the Corten business to the Indian multinational ArcelorMittal in 2003 and no longer produces any Corten, but the company maintains the rights to the name.
There are many producers around that produce weathering steel that is often referred to as Corten. Specifiers wanting the real thing have to pay a little more and for this they get a stamped receipt.
Corten is around three times as expensive as ordinary mild steel plate. Yet looks identical when new, so it’s perhaps not a bad idea to get some verification as to what you are paying for, as the finished look won’t reveal itself for a decade or two.
As a base metal, Corten sheet is similar in price to metals like zinc or copper. It will never compete with the usual claddings like brick, timber and render, but is perhaps comparable with stone or glass.