The main reason that those older rounds don't have disparities between SAMMI and military is that SAMMI didn't exist back then.
The other reason for the differences (in more current calibers) is that SAMMI and NATO spec aren't even always measuring the same things.
They are very close, but in general SAMMI .223 Remington chambers have tighter headspace, and much less freebore before the rifling is engaged. Putting 5.56mm military ammunition in a .223 chamber can cause high pressure. SAMMI chambers are designed for sporting arms where accuracy is generaly more important than absolute reliability.
(Although some commercial semi-autos marked as ".223" may actualy have NATO reamed chambers to increase reliablity, and because .223 in a 5.56 chamber is the "safe" combination.)
If a SAMMI-chambered sporting arm fails, you lose the deer. If a military chambered arm fails, you might lose your life. Although in many calibers SAMMI and military spec. are often in agreement, or at least have lots of overlap in the selection of loadings availible.
A NATO chamber has looser headspace, and more freebore before the rifling starts to aid in reliability, and the firing of differing cartrdige lengths like the .223 tracer.
As a general rule, you can shoot .223 in a 5.56 NATO chamber, but 5.56 NATO should be avoided in a .223 chamber. The 5.56 NATO spec is approximately 10,000 cup higher in pressure than the SAMMI spec for .223. The Tighter chamber, and shorter freebore before rifling begins might drive the pressure difference even higher.
I don't think there's an "offical" SAMMI warnig for .308 and 7.62 NATO though. There the concern is often the opposite, that "hot" commercial .308 made for bolt-action hunting rifles should be avoided in Military 7.62 chambers. Perhaps that's because SAMMI normally concerns itself with commercial arms cut with commercial chambers.