Oh, boy, ammo talk! I won't go too in depth, but for most intents and purposes, 7.62x51m NATO is pretty much the same as .308. The only significant difference is that 7.62x51mm rifles have 0.013" longer chamber specs, so you can get case head separation if you load a factory .308 Winchester ammo into a 7.62 rifle. 7.62x51mm rounds can be loaded to higher pressure than .308, but they should not be unsafe in a .308 rifle.
In short, no significant difference, though you're right that technically, I would want a rifle chambered for 7.62x51mm to avoid any pressure issues.
What you never, never want to do is load 5.56x45mm ammo into a .223 rifle. The ammunition is nearly identical, but the military load is overpressured due to head space/neck issues and can result user harm if fired from a .223 rifle.
In short, buy the military chambered rifle and you can load civilian or military ammo without significant issue, though accuracy may suffer.
How much did you really not care to know all that?