Okay, now that I did play the latest release of Azure Serenity: Tranquil Dreams, I can explain the differences. The original Azure Serenity is an absolutely massive level, albeit one that's somewhat low on detail, with a lot of places only offering a mild level of challenge and most collectables not unlocking anything. The difficulty is mostly normal-hard with only a handful of spots and the finale deserving the label very hard.
Tranquil Dreams is a remake of that level. Although far from finished (any unfinished parts are permanently locked unless you play in open world mode), most of the content that existed in the original has already been fully overhauled. It has a much greater attention to detail, but is also far harder, with the difficulty mostly being hard-very hard, with some challenges even arguably qualifying as lunatic. If it actually gets finished, it's going to vastly exceed the original in terms of size and complexity and easily become the biggest KS level ever.
The original is something I'd recommend to people who are simply looking for a ton of exploration, but not too much challenge. While the remake is aimed at people who want even more exploration, but also don't shy away from a good challenge. It can be worth playing both, as some parts have changed quite a bit due to their altered level design, many swapped music tracks as well as the fact that some areas originally served a completely different purpose.
Also, The Salty Seas is simply the name of the remake's first chapter. It has a complex structure consisting of a gigantic hub where various chapters can be accessed, which are basically levels within the level. Though only the first one is finished so far.