Omni is not a separate chain. Omni is a layer on top of bitcoin and all omni transactions are either recorded on bitcoin's blockchain (exclusively) or transferred via the omnibolt fork of the lightning network.

It has a lot of similarities with RGB but it lacks RGB's privacy features, such as confidential transactions. It also doesn't use single use seals. Both use client side validation but Omni puts a significant amount of client side data on bitcoin's blockchain where anyone can parse it. RGB puts less data on bitcoin's blockchain and instead expects users to send client side data to one another on a separate data transport network.