Yes, asymmetrical tires are common today and you wouldn't believe how many installers get it wrong even when the customer informs them ahead of time.
Personal experience here with Pirelli P7 Cinturato All-Season PLUS(labeled Outside) and G/Y Assurance Comfort Tread Touring(labeled Outside). Even though the G/Y ACTT have the same tread pattern across the tire, it's that one sidewall is stiffer than the other. I guess that G/Y chose to only put one stiffer sidewall on the Touring as to give the driver that little bit extra in the corners without making the whole tire too harsh?