For the end user they both affect the 'feel' of the product - how it behaves on the detail level when in use. "I have a door I have a hard time closing" and "the dynamics feel a bit clumsy" deal with totally different things on the engineering level, but end users (generally) are not buying engineering but holistic products.
Namely, concerning this comment: Are there compromises made on the design of the handling to facilitate the build quality? And if there are, then those are not two different things, but systems which interact - hence, it's relevant to offer commentary on one while discussing the other.
Maybe I'm being overly simplistic here but I'd say if the finished product doesn't match the design then it's a build quality issue, whereas if it does match the design and it's still crap then that's a design issue.
Arguably if they end product doesn't match the design because the design isn't feasible to manufacture then that would also be a design issue.
Ford doesn't compete with Land Rover, Mercedes and BMWs but deliver a good value-for-money nonetheless. Compare that to a Cadillac Escalade from GM: Worse quality than a Ford, priced at Mercedes level.