@Komisar_Kastan , hello and welcome to the Poker Chip Forum! I'll do my best to answer your questions, but I am far from an expert.
Iron Clays are the name of a particular chip made specifically for the gaming market. They are injection-molded plastic with a metal insert. They are not at all related to what the members of this forum call "clay chips".
Almost everyone selling poker chips now calls theirs "clay" or "clay composite". They can do that even though they're made out of plastic because almost all plastic composites contain some amount of minerals. So the people who made Iron Clays weren't lying to their backers - their chips do contain some clay even though they are basically just plastic.
The chips that members of this forum call "clay chips" are also made of plastic. The plastic composite they're made of contains more minerals than other chips, so they're
more clay-like than most chips but they're still just plastic. However, the way in which they're made - compression molding - is a much more expensive process than is used for most other chips (injection molding), which is why these "clay chips" are more expensive. They would probably be far too expensive for you to include in your game.
Apache contracted with manufacturers in China to produce injection-molded plastic chips to their specifications. These are known as "China Clays" because they're somewhat similar to the chips that forum members call "clays". But because they're injection-molded, they're quite a bit cheaper. Unlike compression-molded clay chips, the printed centers are just adhesive labels that are applied after the chips are molded; with compression molding, the printed centers are pressed into the chip during the molding process and are known as "inlays". Compression inlays are more durable and are far less likely to come off than labels on injection-molded chips. That said, most labels are actually quite durable and will rarely come off, assuming that the labels are high-quality and the application process is high-quality.
If you're familiar with contracting with manufacturers of injection-molded plastic items, then you could do the same thing that Apache did and have poker chips produced from scratch to your specifications by a factory in China.
Otherwise, you could use ceramic chips. These are produced as white blanks by companies in China, and then they are printed on by various companies in various places, including China and the US. They can be printed with any design you like. The printing covers the entire face and the sides (also called "the rolling edge") of the chip. There is no label or sticker; the printing is fused into the surface of the plastic chip and is permanent.
Finally, you could use blank chips and apply custom labels. There are a wide variety of blank chips available; they are all made from injection-molded plastic. They come in different weights, and are usually weighted with metal inserts, although some are lighter and have no metal inserts. The blanks come in many different colors and have many different types of designs around their rims; the centers are all plain, as they are intended to have labels applied to the center. They are available from many different sources, especially in China. Many of the suppliers will also print custom labels to your specifications and will apply them to the blank chips before they deliver them to you. This is probably the most affordable method to obtain chips for your game, but you will want to be very selective in choosing the right kind of blank to complement your label design.
If you have contacts in the board gaming industry, you might try to find the people who produced the board game Splendor. That game had at least three different types of chips made: the first edition had heavy chips with metal inserts and labels; the second and later editions had lightweight chips with labels but no metal inserts; and they produced a premium set of chips used as convention promotions that had translucent chips with labels and metal inserts. I believe in every case the blank chips were custom-produced to their specifications (especially with respect to color) but they may have used some standard molds that the manufacturer already had. If you ask them, they might refer you to the sources they used to produce their chips.
And, of course, you could reach out to Roxley Games, who made the Iron Clays. Those look and feel quite a bit different from most of the chips I've described so far, and they may be the most appropriate to emulate for your game. Iron Clays are injection-molded and have metal inserts, similar to most cheap blank chips, but they are fully custom rather than using a blank and applying a custom label. Unlike ceramics, their graphic design was not printed onto the chip; instead, the graphic design was molded into the plastic using injection molding with two different colors of plastic. This definitely required custom molds. This probably made them more expensive, possibly too expensive for your game. But if you can, you should ask them what they did and who they worked with.
I hope this helps! Let me know if you have further questions and I'll do my best to give you guidance.