Both relationships exist, and this is a question that has confused me for years now. Is “design” intended for the design of the artwork and not something like “acoustic design”? If so, how would it mean something different from “graphic design”? And if it doesn’t mean anything different, how come we have different relationships for the exact same thing?
Most designers are credited differently for different releases for what apparently is the same work.
I have brought this up to @reosarevok before, but I think it got buried. I can’t find it anymore, anyway…
But I found a related ticket while searching!
The only case where I can imagine a difference is if “design” is meant to encompass other types of design, like industrial design. e.g. someone designed a nice chair pictured on the cover 
It’s a yes from me, to merge, unless someone comes up with a common scenario I haven’t thought of.
Honestly, the answer is “I have no idea to know if they’re the same thing”. If “design” is always equivalent to “graphic design” then ideally we’d keep just one of the two - just not sure which!
I think probably merge into “design” (I think there aren’t enough other something-design music credits to make it confusing?) and use the “graphic design” description, which makes it clear that it’s about arranging visual elements.
Credits in a booklet change a lot. “Design”, “Graphic Design”, “Booklet Design”, “Packaging Design”, “Cover Design”, “Design and Artwork”. Sometimes only parts of the design.
As “Design” has the option to write in the task then I don’t see an obvious need for them both. The specific design task can be written in where it has been noted.
Personally, I’d prefer “graphic design” because it’s more specific. Presumably the reason there’s both now is that somebody looked for graphic design and couldn’t find it. Whereas, if you look for design, you’ll find graphic design and think “what other design could it be?”. “Design” without a description can always lead people to think it can mean some other kind of design.
But, I do think the task field is useful, like @IvanDobsky said. So I’d suggest changing the name of the current “design” relationship to “graphic design” and merging the current “graphic design” relationship into it.
But frankly, I’d take either one; I just think the current situation makes no sense.
There are many releases where design & graphic design are both artist credits. Typically, graphic design has to do with the layout, typography, etc. But yeah, not sure what design would mean when I see both present on the same release. I’d say just leave it like it is and credit how it’s in the booklet. If it says design, just use that. If it says graphic design or layout, use graphic design.
Do you have some examples we can see? Because, either:
I also don’t know what (if any) difference there is between the two, but I also remember seeing both credits on the same release
edit: looked through my collection, and I found one, kinda… it has credits for design and “graphic artists” (entered as Graphic Design in MusicBrainz)
That is a good example: “Art Direction and Design” is the person doing the layout. The lead (or maybe the company in this case). “Graphic Artists” are the people creating the components. Editing those images and fonts.
Though I would have put the “Graphic Artists” down as “Artwork” (but I think that currently lacks the ability to write in the specific task)
I can’t figure out how to search for a release that has both. Maybe there aren’t as many as a remember, but it seems like I’ve run across these many times. I definitely wouldn’t be opposed to combining them if we can write in specific tasks.
I think some generalized design credit is warranted for special cases where the release doesn’t come in standard packaging.
There’s a release by the Flaming Lips that has a USB flash drive embedded in a gummy skull: Release group “Gummy Song Skull” by The Flaming Lips - MusicBrainz It would make sense to me to distinguish the graphic design for the packaging and the sculpting for the skull.