I don't really understand or appreciate a distinction. The seL4 design was used as a starting point and small changes were made mostly as a matter of API convenience. I consider the design of an operating system to be by far the most difficult part, and the typing to be less impressive/important.

Helios hasn't done anything novel in terms of operating system design. It's taken an excellent design and reimplemented it in with a more modern language and built better tooling around it. I tend to point people towards the Helios project instead of seL4 because I think the tooling (especially around drivers) is so much better that it's not even a close comparison for productivity. It's where the open source OS community should be concentrating efforts.

Usually "based on" means the original codebase is mirrored/extended. Arguably if what you say is true, that is Helios' design has minor differences to seL4, then "based on" in reference to the design is indeed better description than "inspired from" which makes it sound (imo) to have significant changes.

"... whose design is based on it" would seem to cover all the, er, bases.