You (or I) are probably not ever going to be able to tell the difference by looking at copies and we'll probably not have much of an opportunity to ever see an original up close.  

As to the S and G being a "type" of violin.  No, they simply denote the maker(s) of these instruments and probably more closely denote a "pattern" for the body of the violin. Keep in mind that these instruments weren't mass produced and each one is a distinct work of art. People have taken the exact measurements of many of them and modern companies use those measurements to create violins that can replicate the dimensions of the originals.  Modern cubic zirconia look like a diamonds, but they are not.  Likewise copies of S's and G's illustrate that there is much more to a great violin than a pattern.    

In terms of construction, the lower bout of a G. is a bit wider than a S. with a slightly fuller waist.  We're talking 1/4 to 1/3 or an inch so your probably not going to be able to tell.  The original G.s were sometimes a bit lopsided (or so I'm told.) and the F holes more angular. 

The G.s have a reputation for having a better low end than the S and likewise the S has a reputation for having a better high end.  The G.s are supposed to be louder and harder to play. 

Here's a head to head: 

PopFiddle said
The differences are subtle, but real to the discriminating violinist.

I think the differences are fairly noticeable, as in term of violin dimensions which (assuming everything else is the same "ideally" just for comparison purpose) related to the "typical" sounding characteristics of those famous makers' violin copies.

As previous posters mentioned, some differences are decorative and some are for the purpose of enhancing particular violin sounds/characters.

As FM mentioned, Stradivarius's violin form/dimension is the most copied, so is the best solution strategy for dealing with certain setup/tuning problem, as each violin form/dimension, while enhances certain sounding characters does come with its own issue/problem of fine tuning the instrument.

Agree with @Uzi about Strad vs Guarneri (also typical sounding characteristics) that the violin is a bit  wider and deeper, as to increase its internal volume. Amati does that by higher center, and furthermore in Stainer, as @Tucson1 mentioned, Maggini is both by wider and longer body.

While trying to do setup/tuning my violins a while back, I did some sound samples (served as subjective comparison of/tuning point for further improvements) of a Guarneri, Amati, Stainer and Maggini copies to post for members evaluation/comment/advice (just in chat box, not in the forum).

Also there are some differences in copies as well. A so called "master copy" is a faithfully reproduce of the original to minute details, while a "good" copy will almost follow everything especially its dimension or anything having to do with sound production, then there is "hybrid copy", taking a mix of two or so of those famous makers creations.