Faux clays aren't made any more; they're a specific line of chips that were made quite some time ago and attracted a good bit of enthusiasm but have long since been sold out of any retail stores. If they were made today they'd probably be considered "china clays". If you want faux clays, you'll have to turn to the third party market, i.e. the PCF classifieds. You probably don't want them, though - they feel pretty nice, but they're very plain in appearance.
China clays are, basically, any injection-molded chip that is made to resemble a real clay chip in appearance, weight, and feel. They're definitely not the same as clays, but they're kind-of similar; some look and feel more like clays than others do. They're injection-molded but they don't have a metal insert.
There's been several different lines of china clay chips; many of them are no longer made and have sold out of retail stores, so to get any of those you'll have to turn to the classifieds. Examples include Spirit Molds, Championship Poker Series, and Progen 80.
Newer china clays are still being produced, or at least are still available in quantity in retail stores. Examples include Milanos, Majestics, and Royals. Apache is your best bet to find these; if they're sold out of something you want, you can maybe find them still in stock with a vendor on
eBay or
Amazon. If not, then once again you can try the PCF classifieds. They don't get listed for sale as often as clays, but if you put up a want ad someone may decide it's time to get rid of their china clay set and contact you.