"До скорого" is short for "до скорого свидания", i.e. basically the same thing but with a bit greater certainty and less formality. On a literal level, it's like "see you soon" vs "see you", but it's pointless to use literal approach for such things. The only thing that matters is how people use these phrases.
Both sources you quoted are broadly correct.
"До свидания" is a standard, plain and somewhat formal "goodbye".
"До скорого" is the closest in meaning to "see you soon", but can be used in any similar context. You'll hardly find it in formal writing; it's less reserved and friendlier but still rather polite. In usage, it's closer to "see you" rather than to "see you soon": like the former, it's an 'incomplete' phrase with an implied ending.
"До встречи" is technically very similar to "до свидания" (встреча и свидание are almost the same thing). But because "до свидания" is very neutral and standard and does not imply anything, replacing it with "до встречи" implies that you actually intend to meet later. This is why "see you soon" is a reasonable fit, although in modern English it hardly implies such intention anymore. Unlike "до скорого"/"see you", it is a complete sentence, and thus feels a bit more formal.