If a rifle is a particular calibre, say .308, then yes whether it is old or new the same ammunition will run through it. Of course, firearms can tend to only like a particular type of ammo, a particular brand for instance.

I make my own ammo so do a load development of the perfect round for it and then make that round, over and over again, exactly the same. Factory made ammo is made on mass and is quite often not exactly the same. This variation, at long range, can mean a miss.