Ignoring the sentence that admits they can be the same ("Programmers work closely with software developers, and in some businesses their duties overlap.").

Programmers is like a translator; somebody else came up with what to do and you're doing the mechanical work of converting words into C++.

Developer involves coming up with what to do.

Hence programmers is a lower paid position.

Programmer as defined here, in my experience, is a job that has never really existed. Sure, they've tried many times to create this divide - going back to the beginning of programming (originally considered secretarial work) - but ultimately programmer is still making many design decisions when typing out code.

Your interpretation seems like apophenia to me.

There's no functional difference between a 'software developer' and a 'programmer'. they're just synonyms that sometime pay differently.