German/Israeli K98 Mauser

.308 is fine to shoot in a 7.62x51mm designed rifle. But you cannot shoot 7.62x51mm NATO in a rifle designed only for .308.

Same with .223 and 5.56mm
Incorrect about .308 and 7.62 NATO. .308 is hotter (and shorter) than 7.62 NATO. However, 5.56 NATO is hotter (and longer) than .223 Win. Feel free to look it up.