It entirely depends on the particular workplace and what is involved, but either way a decent manager should work with you.
"John, Sarah, and James have already asked for that time off, and we have to have someone in the shop. Would you be able to change to this time to this time?" And you never, ever, ever call someone in when they are on PTO. If you, as a manager, okayed it, it's on you if there's not enough coverage for whatever reason.
In fairness, I work in Search and Rescue, so operations like mine and other emergency-related workplaces can't just be like "Oh well, I guess we won't have coverage that day, Joe wanted to go hunting." If you work in an office and your work literal lives aren't depending on you and others being there, then managers should work around it as best they can.