What are the the different string ball end sizes for a violin? Specifically, what does "Size Gold E String Ball End" mean?
You're missing an important distinction between those two links. The more expensive one is a full set of violin strings, while the less expensive one is just a single E string.
The Obligato brand appears to be a single line of products from the Pirastro company, so I would not expect to see competing feature sets as long as you're choosing the product correctly (i.e. getting the right string, and choosing ball end or loop end depending on your instrument configuration.)
I think adding commas should help.
Pirastro Obligato, 4/4 Size, Violin Strings, 4/4 Size, Gold E String, Ball End
I think this one is cheaper than other because only the E string contains precious metal. The other set has a Gold E, and Silver D and G.
As far as I know, all "Ball End"s are going to be similar (if not the same) in size.
I looked this up and if you look up Ball End Adapters which are sold on the same site as the strings you were looking at it describes the adapters that you need for strings with ball ends, if you don't want to put the ball into an adjuster.
The cheaper price is for one E string with a ball end.
I suspect that the set of strings which is the more expensive price contains only 1 string that has a ball end. The rest may well have loop ends. I think that these strings may be designed to be used by people who don't want to have adjusters on their tail pieces. However I don't know why anyone in this position wouldn't just buy a set of loop end strings. It is possible that the set gives a player the opportunity either to use an adjuster for the E or to use it with an adapter.