It's pretty simple, actually:
Hiring for Culture - generally means you're looking for people who are like you - or like your brand - or have something in common with your corporate values. This generally gets a bit fuzzy pretty quickly, and is full of "like us" bias. There are people who are hiring for culture effectively, but there are many more train wrecks out there who do it poorly...
Hiring for Motivational Fit - means you're donig a deep dive of when a candidate has been satisfied and unsatisfied in their career, then you're doing an objective assessment on whether your company, hiring manager and open job can provide the good stuff the candidate finds satisfying without a lot of the bad stuff that doesn't satisfy them.
One is cloud level, one is street level. When in doubt, go for motivational fit. It's what will deliver true retention over time.