Hey there !
Lucky you, here is a brand new, thorough, sexy Astro guide :
https://docs.google.com/document/d/1...lWUm4JjAI/edit
If you like getting in depth of things, this is to be your bible

I can try to give you a general presentation of AST compared to WHM though. WHM's focus is regen heal, with little to no damage mitigation. Basically you heal after the damage, except for Divine Benison for single target shielding, and Regen which kinda works as compensation of ongoing damage (auto-attacks on the tank for instance).

Benefic and Benefic II are your Cure I and Cure II.
Helios is your Medica (it heals more than Medica).
Earthly Star is an AOE you set up on the ground, and everyone standing in it will be healed when it pops (at the end of its timer or when you pop it yourself), it's free (no MP cost), and it also damages enemies standing in it. Essential Dignity would be your Tetragrammaton in an instant heal, but it works differently as it heals more the lower the target's HP are. So you can play with your tank's sanity with "How low can you get?"
Your DPS kit is limited. Malefic is your Stone (faster cast time), Combust is your Aero II, Gravity is your Holy (but weaker and no stun effect).

Main difference : sects and aspected spells. You have two sects, Diurnal (Regen) and Nocturnal (Shield). That gives the added effect to the Aspected Benefic (single target) and Aspected Helios (AOE). In Diurnal Sect, you Aspected Benefic is a WHM Regen (though shorter duration, High MP cost) and Aspected Helios is Medica II. In Nocturnal, these two spells will place a shield for respectively 250% of the heal on a single target, and 150% of the heal in an AOE.

Then you have AST only kit actions, cards and buff timer manipulation that are covered in that guide. Everything I said is quite general, if you look in the details there are significant potency differences on each spell / abilities.

Hope this helps!