They are NOT the same cartridge. Although similar.
You can put 7.62x53R in 7.62x54R... But not the other way around unless you want to prematurely wear your bore down. Basically the 54 will fire in the 53, but wear the rifling and some might not even chamber.
But if the rifle has been used a lot - it won't mater. In that case, they are interchangeable.
I have some boxes of 7.62x53R lapua Ammo... Not sure if they even make it anymore.
Here are the basic differences.
Differences between 7.62x53mmR (Finland) and 7.62x54mmR (Russia)
Round length: 77.00 mm (54R: 77.16)
Case length: 53.50 mm (54R: 53.72)
Rim diameter: 14.40 mm (54R: 14.48)
Bullet diameter: 7.83 mm (54R: 7.92)
Your P26 should be 7.62x53R... Unless marked by the Finns as otherwise or shot out enough to take 7.62X54r. The Finns also used captured Russian Ammo in their rifles. Long story short, it's ok to use if it chambers, but 7.62x53R would be more accurate (likely) in your rifle.
Here is more info - please read it.
About the 7.62x53R
https://en.m.wikipedia.org/wiki/7.62×53mmR
About the 7.62x54R
https://en.m.wikipedia.org/wiki/7.62×54mmR
Hope that helps.