What is the name for type of symbiotic relationship that small black and blue fish has with big orange fish?

You're describing a classic example of mutualism.

Here's why:

* Small black and blue fish: These are likely cleaner fish, often brightly colored to signal their job.

* Big orange fish: This is likely a larger fish that needs cleaning (like a grouper or wrasse).

Cleaner fish remove parasites and dead tissue from larger fish, providing a valuable service. In return, the larger fish provides protection and a source of food scraps for the cleaner fish. Both organisms benefit from the relationship.

Other types of symbiotic relationships:

* Commensalism: One organism benefits, while the other is neither harmed nor helped.

* Parasitism: One organism benefits at the expense of the other.

Let me know if you'd like more details about any of these relationships!