Engaged core in pilates=mula and uddiyana bandha in yoga?

Hello, I practice both yoga and pilates. I’ve been practicing my mula and uddiyana bandha (switched from vinyasa classes at the studio i go to to ashtanga & hatha classes, which focused much more on the bandhas in stillness). I’ve also been practicing pilates for about the same amount of time and am still practicing engaging my core correctly. My question is, is engaging the core (lateral breathing, drawing belly button in while lifting the pelvic floor) the same as the bandhas? BarreBody pre and postnatal course (which I am taking) seems to indicate it is.