Snake Chain and Omega Chain are similar types of jewelry chain that aren't really chain at all. The core of an omega chain is either a long wire or a woven mesh. Then the chain creator takes small metal plates or disks and attaches them to the core.
Sometimes jewelers and jewelry stores use "snake chain" and "omega chain" for the same jewelry chain. When first researching snake and omega chain, the difference seemed to be that snake chain is round, and omega chain is flat. However, the actual difference seems to be in the structure. Snake chains are typically made of wavy plates, wehereas omega chain plates are flat. Also, snake chain plates are typically joined to each other, but omega plates are joined to a wire core or mesh inside the chain. A snake chain may also be found labeled as "Brazilian chain."
You may see Omega chains sold as "flat snake chains," and you may see snake chain sold as "round omega chain." You may also see a "half round" omega, which is domed, a cross between snake and omega. I would guess it's more a factor of the vendor being familiar with only one of the terms, or simply trying to be clear about the product. Whether it is called a snake or omega, if it's called flat, you should receive a flat chain; round, round.
These chains are extremely popular for wearing pendants, but remember to make a large bail so that your pendants will fit over the clasp, as well as a wide chain. Flat omega chains can be quite wide, 4mm or even greater! Snake chains are generally more flexible than omegas, because they typically don't have the core wire or mesh that omega chains do.
Most snake chain and omega chains come finished - that is, with a clasp attached. Because there are no real "links," unfinished snake or omega chain must have the findings soldered on.