Yamato declares before attacking Kaido that she'll sail with Luffy. He says she'll never leave even with her cuffs gone.
Momo declares before attacking Kaido that he'll become shogun.
Along with the other contrasting parallels, they have a clear contrasting goal. One has been stuck in Wano and wants to leave. The other has been stuck outside of Wano and wants to rule it. Neither of them has questioned or second guessed their goal.
I've shown this before, but Oda paralleled this scene to show it's the same. If Momo becomes shogun after the war (which is obvious), Yamato is achieving her's of going out to sea (should also be obvious). She wouldn't rant about unleashing the samurai into the world if she wouldn't be part of them.