Omise and OmiseGO are offering two different products. This sometimes disturbs why Omise supports OmiseGO and there are many intersections between the two.
Omise was created with an e-payment solution similar to Paypal and Stripe, but focused on the markets of Southeast Asia and Japan. Its purpose was to be able to legally manage credit cards because it is fully compatible with PCI standards while Omisego can be described as the blockchain version of omise.