For what it's worth there are some "A" 7mm Mags. There were in the first 3 years of the #1, 1967 through 1969.
The "A" as mentioned is the Light Sporter, with a 22" barrel, adjustable sights and the Alex Hnery Forearm. There are probably well less than 50 in this configuration.
The are also about the same number of non prefix #1s in 7mm Mag in "AH" or the Light Sporter, without sights and the Alex Henry Forearm.
There are also "AB" non prefix 7mm Mags. the same light 22" barrel with no sights and the Semi Beavertail Forearm.
The "S" is essentually the same rifle but with the 26" medium weight barrel. The "S" has the same barrel length, weight and contour as the Standard Sporter but the Medium Sporter has the Alex Henry Foreend along with the sights and the barrel band for the fromt sling swivel.
To the best of my knowledge there are no "S" rifles in 30-06. Even in the non prefix rifles I have never seen one.
Simply measuring the length of the barrel should tell you what you need to know. That and the existance or adsence of factory sights will determine the rifles configuratiom.
If there is any question a call to Rugers Records department wwith the serial number will give you the shipped configuration.
Some of us, Okay, Splitz and I at least consider the "S" the most classic of the #1s. A "A" in 30-06 and and an "S" in 7mm Mag would be a nice "set" of rifles. ;-)
Now an "S" in 7mag and a 243 "A" that wuld cover nearly everything.
the best
Ross