This saying builds upon the idea that there is a clear difference between doing the right thing vs doing things right.
Doing the right thing
Doing the right thing emphasizes the value of picking the right thing to work at. In case of conflicting priorities, it’s vital to be able to decide which activity to focus on.
Doing things right
Doing things right instead emphasizes the value of doing something “by the book”, or thoroughly and with great attention to detail.
Deciding between the two
As with most hard things in life, there is no silver bullet. Both angles have benefits and drawbacks depending on the context.
If anything, categorically sticking to either one will likely end up being negative regardless of which one you pick. Instead, think of it as a sliding scale where circumstances and context will make it lean in either direction.
Our ability to know when to favor which one will often have a big effect on the outcome.