Yes, yes you do.
Manual brake cars have studs pressed through two sheet metal firewall sections.
Power brake cars have studs on the booster mount that go into the cowl.
Completely different.
...and if you can get the studs to come out of that sheet metal sandwich without destroying the cowl...you're a better man than I.
No, you don't.
The difference is not in manual/power brake cars, the difference is in A & B body cars.
A bodies have studs pressed into the brake pedal frame assy, which then comes through the firewall and the master (manual) or booster bracket (power) slides onto those studs and gets attached with nuts.
On B bodies, there are no studs on the pedal bracket assembly. The manual master cylinder has 4 pressed-in studs that go through the firewall and pedal bracket (and reinforcement plate, if present) and attached with nuts from the inside.
For power brake B bodies, the booster uses no bracket and the studs on the booster go directly through the firewall and pedal bracket. The exception would be hemi cars or if you decide to use the A body bracket due to clearance issues.
When a power booster is used on a B body, it will use the A body style master (no studs, or remove the studs from your manual brake master cylinder) in order to bolt to the booster.
The issues start when you try to blend A body and B body parts. But since the OP is talking about switching parts between two different B bodies and NOT an A body/B body swap, it becomes a straight across bolt-in.