If the rifle was re barreled using an aftermarket barrel such as Shilen or similar the barrel will not have any warnings like a factory barrel. None that I have ever seen anyway. Here is an example of my originally Remington 700 series (Model 725 222 Rem.) blued action with a stainless heavy .223 Remington barrel. The replacement barrel only has the caliber marked, that is all.
Barrel makers like Shilen, Kreiger, Leija, Shaw and the rest do not mark the barrels. The smith doing the work would label the caliber or should anyway. If the barrel started as a blank it would only have a bore diameter for example .308 the smith would cut the chamber such as .308 Win, 300 Win Mag or whatever .308 diameter bore he chambers the barrel for. Barrels also normally do not have a manufacturer name stamped on them, not the ones I have worked with anyway.
Ron