No.
In short, you don't want to trust inch designations of bicycle tire sizes, they offer plenty of chances to get it wrong.
The least messed up tire sizing method is the ETRTO system, which gives sizes in millimeters based on approximate width and the Bead Seat Diameter (where the reinforced lip of the tire meets the rim).
"Old" 27" is 630 mm ETRTO Bead Seat Diameter. "New" 27 is a rather silly name being used for 584 mm ETRTO AKA 650B (mainly) mtb wheels.
All 700C-something tires are meant for 622 mm ETRTO rims, what the MTB industry for some strange reason has decided to call 29er AKA 29", in a vague reference to the diameter of the wheel with an inflated tire fitted.
700C / 622 mm is the most common size for road bikes, with "old" 27" / 630 mm being an earlier road bike standard.
There's some cross-compatibility between 29er tires and 700C road tires, unless they're too far apart in width. A real narrow road tire won't fit well on a wide MTB rim, and a road bike frame/fork may not have the clearance to take a wider MTB tire - even if it would sit just fine on the rim.
I'll post a link where you can read up more.
The recommended tire size for a bike that requires a 27 x 1.25 tire is 700c x 32mm.
The recommended tire size for a bike that requires a 27 x 1 1/4 tire is 27 inches in diameter and 1 1/4 inches in width.
The best brand for a 27 x 1 1/8 bike tire is Continental.
MAYBE - , frame size has nothing to do with tire size. Style does, and if its a mountain bike, it will not work with a 27 (road racing) wheel and tire. Brakes will not fit.
The equivalent size of a bike tire that is 27 x 1 1/4 is 700c x 32mm.
The size of a bike tire that is 27 x 1 3/8 inches is 27 inches in diameter and 1 3/8 inches in width.
For a tire that is 27 x 1 1/4, you should use a bike tube that is 27 x 1 1/4 in size.
The recommended tire size for a 27x1 1/4 bike tire is 27 inches in diameter and 1 1/4 inches in width.
The best brand of 27 x 1 3/8 bike tire for long-distance cycling is Continental.
A 27 x 1 1/8 bike tire is equivalent to a 700 x 28c tire in a more commonly used measurement system.
The recommended tire pressure for a bike with 27-inch tires is typically between 80-100 psi (pounds per square inch). It is important to check the sidewall of the tire for the specific recommended pressure range.
The best tire options for a 27-inch bike would typically be 27-inch tires that are compatible with the specific type of riding you plan to do, such as road biking, mountain biking, or commuting. It's important to consider factors like tread pattern, tire width, and durability when choosing the right tires for your bike. It's recommended to consult with a bike shop or do some research to find the best tire options for your specific needs.