So, I understand short or long cage derailleurs have different chain wrap compatibility, max cog size and so forth. Below is where I am confused:

Cassette Compatibility - 10
Maximum Sprocket - Low sprocket: 34T / Top sprocket:12T (front double) / 20T Low sprocket: 32T / Top sprocket:12T(front triple)
Minimum Sprocket - Low sprocket: 28T / Top sprocket:11T (front double) / 20T Low sprocket: 25T / Top sprocket:11T(front triple)

That is for the GS tiagra RD

Cassette Compatibility : 10
Maximum Sprocket : Low sprocket: 28T / Top sprocket:14T
Minimum Sprocket : Low sprocket: 25T / Top sprocket:11T

That is for the SS Rd.
What I get is the max cog for the SS is 28, for GS is 34. Can anybody explain the rest?

Let's take the SS for one example. The cog capacity numbers have to do with distance from the pulley to the cassette. At the top cog it can manage a 14T without running too close, and an 11 won't be too far away to shift well. At the bottom, it can manage a 28 without running too close, and a 25 won't be too far away to shift well. With 11-28, the rear takes up 17 teeth of wrap, leaving 33-17=16 teeth difference for the front, matching the 50-34 front rings.

If you compare the same model of RD side by side, you can barely notice the angle at which the body of the GS travels is slightly steeper than the short cage model. This lets it get to a larger cog without running into the cassette. The longer pulley cage lets it handle the extra chain.

That makes sense, and then I get the general idea for the GS as they are giving an example for running it with a triple, but:

Maximum Sprocket - Low sprocket: 34T / Top sprocket:12T (front double) / 20T Low sprocket: 32T / Top sprocket:12T(front triple)
Minimum Sprocket - Low sprocket: 28T / Top sprocket:11T (front double) / 20T Low sprocket: 25T / Top sprocket:11T(front triple)

In the above example, what does the 20T refer to?

Probably the front difference though it's not entirely clear from how your copy/paste turned out. Try looking at it in tabular form here 2016-2017 SHIMANO Product Information Web

Nah, it doesn't make any sense there either.

RD-4700-GS

My cut and paste is how it looks on Shimano's consumer page, as well as any vendor that just copies and pastes that info from there. Tabular data makes sense to me, their way of listing it as shown above is what is confusing.

Maximum sprocket - the biggest rear sprocket RD can hadnle.
Top sprocket - the smallest rear sprocket RD can handle.
/N T - the maximum difference between the teeth no. of the biggest and the smallest rear sprockets.

The other two numbers are for triple front chainrings.

However, sufficient (and often available) data is just max and min. rear sprocket accepted and total chain wrap in number of teeth. In order to make this post a bit shorter, I'll just pass this link where I've already explained it all in detail, with some examples:

Rear derailleur

(the paragraphs explaining are: "Derailleur capacity – cage length" and "Rear cog size limit")

Yeah, actually the link that Darth Lefty posted does make sense, the page I was looking at (the same as yours I assume) doesn't. I assume the 20T thrown in there refers to the maximum difference between the front rings.