Here.
A52 is their main classless server meaning you can pick and choose every skill/talent/enchant every level but since its been running for 9 years and has tons and tons of hyper mudflation it can be super overwhelming. There are a few dozen "archetypes" ie new classes you can choose and level as which is the best way to play it especially starting out.
Elune is the seasonal server which the gimmick is random fucking skills, just pure RNG, some minor control/customization but you can end up with shadowbolt one level then thunder clap the next.
Both of the live servers are on TBC as of now, and 3.3.5 client
PTR Servers:
Grizzly Hills (Wrath Alpha): This is testing wotlk content, standard A52 stuff custom classes etc, this is just for testing northrend.
Conquest of Azeroth (Alpha): This is just testing a completely different set of custom classes, this is mostly A52 but a different class list, a new dev joined the team and basically did a bunch of custom classes so this is his test server.
Bronzebeard (Warcraft Reborn Alpha): This is a classic (Not vanilla) + server focused on the original 9 WoW classes and focused on open world exploration. this will progress vanilla > tbc > wotlk with custom content/open world stuff but as far as the whole classless/build your own set/archetype thing this is the least Ascension like server, it's focus is on the original 9 classes.