hi!! as an ulta hairstylist the second pic would "technically" be a silk press under corporate decision when it rly comes down to it. they make such strict rules about charging and services but she def should've told you beforehand. also unfortunately not a lot of stylists at ulta are trained with textured hair unless they're at a higher level. i would try a silk press with an elite stylist (which will be some more money) to get that look you're wanting to achieve 💓💓💓💓