True enough, but like I said, it's a matter of emphasis.
I'm most familiar in performing the second stretch (the one lying down) when applying slight pressure to the bent leg to target the glutes. If you focus instead on pressuring down on the dangling leg, then yep, the hip flexors on that side will be targeted.
With the lunging version, it's already targeting the hip flexors primarily. To engage the glutes more, you'd need to lean into the forward leg more.
Forgive the analogy, but it's the difference between doing a leg press with just the balls of the feet vs. driving through the heels only. Same exercise, just slightly tweaked depending on what you want to do with it.
But I think we're on the same page.