(different circumstances have different nuances about what "better" means, it isn't always performance optimization; some do substitute "faster" for "better" here, but I think it loses generality then).
I always heard the "Make it Right" as "Make it Beautiful", where Right and Beautiful would mean "non-hacky, easily maintainable, easily extendable, well tested, and well documented"
My mentor used say it is the difference between a screw and glue.
You can glue some things together and prove that it works, but eventually you learn that anytime you had to break something to fix it, you should've used a screw.
It is trade off in coupling - the glue binds tightly over the entire surface but a screw concentrates the loads, so needs maintenance to stay tight.
You only really know which is "right" it if you test it to destruction.
All of that advice is probably sounding date now, even in material science the glue might be winning (see the Tesla bumper or Lotus Elise bonding videos - every screw is extra grams).
Making it work can be a hacky, tech debt laden implementation. Making it right involves refactoring/rewriting with an eye towards maintainability, testability, etc etc
In ML, often it does work to a degree even if it's not 100% correct. So getting it working at all is all about hacking b/c most ideas are bad and don't work. Then you'll find wins by incrementally correcting issues with the math / data / floating point precision / etc.
Depends on your definition of "right" and "work". It could be a big ball of mud that always returns exactly the required response (so it 'works'), but be hellish hard change and very picky about dependencies and environment (so it's not 'right').
