Both are not coercion. One is paying poor (cash hungry) men for something irriversible they may later regret. The other is providing education to poor women, and empowering them so they will (statistically) decide to have less babies.

Coercion is waaaay less, to the point that I'd like to say educating is not coercing. Education can be undone, unused, forgotten. Vasectomies not so much. I dont think "totally" suppressing reproduction is what happens: those women still want/can/will have babies, just not so many.