INTEGRITY-178B and seL4 are not related in terms of their source code or origin, though they do both aim at the same target audience (security and/or safety-critical systems).

I don't have a good knowledge of INTEGRITY-178B, but as far as I can tell some differences are:

* INTEGRITY-178B is a static separation kernel. seL4 can be used as a static separation kernel, but also allows for dynamic systems, for instance with processes being created and torn-down dynamically at run-time;

* INTEGRITY-178B has a proof that a model of the code satisfies particular security properties, while seL4 has a proof that the actual C implementation satisfies particular properties;

* INTEGREITY-178B is certified to EAL6+, while seL4 has not undergone any external certification process. (Without having a good knowledge of EAL6+, my suspicion would be that the code-level aspects of seL4 would meet or exceed EAL6+ certification, while the process-level aspects would need work on the seL4 side.)

If someone has worked with INTEGRITY-178B, please correct me if I have made any mistakes.