Bakelite is one of the early plastics (along with Celluloid and Galalith). Bakelite is a brand name, named after its discoverer Leo Baekeland; it's more generically known as "phenolic resin". Phenolic resins are made by reacting phenol with formaldehyde. Catalin is also a phenolic resin. Chemically, Bakelite and Catalin are the same, but the two materials are produced in different ways.
In Bakelite, the resins are solidified, then crushed into powder. The powder is then put into a mold; the plastic is then cured in the mold under high heat and pressure, producing the molded part. The final product is strong and durable, and is highly resistant to heat, chemicals, electricity, and mechanical wear. The powder is usually mixed with a variety of fillers prior to being molded; those fillers improve its durability. Because of the high heat that's used, Bakelite is usually opaque and has dull colors since the fillers turn brown or black under the heat.
In Catalin, the resins are kept liquid, then poured into cast shapes such as blocks, sheets, and rods. The cast resin is slowly heated, and after a long time cures and becomes solid. The solid shapes are then machined into their final form; for example, with poker chips, the rods are sliced into discs and then each disc is lathed into the desired shape (usually with a slight bevel on the edges) and polished to a high shine. Because the Catalin resin is heated slowly, it can be colored as desired, including left transparent or translucent. And because the resin stays liquid until fully cured, resins of different colors can be swirled together to create a marble effect.
Bakelite and Catalin are just two brand names for similar substances. Phenolic resins were very handy and were used for a wide variety of both practical and decorative objects, and so were made by a large number of manufacturers, each of which applied their own brand names to the material. And so, you can find a lot of vintage objects which
technically weren't Bakelite or Catalin because they were made by someone other than the Bakelite Company or the Catalin Company, but common practice today is to call anything made from phenolic resin "Bakelite" if it's solid-colored, dull, and molded and "Catalin" if it's colorful, marbled, and machined from cast shapes.
When it comes to poker chips, as
@mtl mile end points out, these were made just for the home poker market. At the time, "pro" poker venues such as clubs and card rooms were using poker chips made from "clay composition", which were mainly celluloid with clay filler. My guess is that clay chips were easier to customize with features like inlays and hotstamps, which helped professional gambling venues protect against counterfeits. Bakelite and Catalin chips were all more-or-less the same, and any customization of them was rare.
As a collector, I think Catalin chips are quite attractive. Compared to modern poker chips they're very light, very slick, and awkward to handle, but I appreciate them for their appearance, style, history, and novelty. Building a set of them is annoying, though. They're widely available on
eBay BUT they almost always only come in three colors: butterscotch, red, and a very dark greenish-blue. The annoying part is that because these chips were made by many different manufacturers over a long period there is a
huge amount of variation between batches. Even though they're all
basically the same three colors, each different batch is going to be a
slightly different shade; color matching between two different lots on
eBay is hopeless. Same thing with sizes - they're all
basically the same size (1.5 inches) but any two given lots are likely to be
slightly different sizes. If you want a consistent set, you pretty much have to buy the set all at once; mixing and matching will be a nightmare.
There are also plenty of Bakelite chips on
eBay; as a collector I'm completely uninterested in them. They're plain, dull, ugly, and boring.
Also, bear in mind most
eBay sellers have no idea what they have, and will happily call nearly anything "clay", "bakelite", "catalin", or all three at once even if they're actually made of, for example, acrylic or polyester like the cheap crappy injection-molded interlocking chips that started showing up in the sixties.
Hope all this has helped somewhat in understanding and appreciating your new poker chips! Welcome to the forum.