You are correct. The spells gained from the cores, are just added to your spell list. The Core Spells are Sun (Bolt / Beam / Burst). DD Also has SLAs like other casting trees, it has Nimbus of Light, Searing Light, AoE Good Damage spell, and AoE Fire Damage spell. He is correct that Searing Light is an SLA in both cases. I also wish to know how the cooldowns of these two identical SLAs will interact. (As I have a 16 DD Cleric / 4 FvS Light SLA Laser Beamer, and will 99% certainty be taking Sun Domain)
Also I, like many others, would like to know how current clerics and FvSs gain this. Free Fred Feat Fun For Few Fleeting Fortnights?
Also to the person or persons who said that using Turns for damage wasnt "PnP' enough, in 3.5 it was I believe either a Feat, an ACF (Alternate Class Feature) or possibly both, to get damage on to your turns. I believe the options are in Complete Divine.
One small nitpick / thought, about both the favored soul and the cleric, getting +10 hp per level seems strong. Like, that's more HP than a Paladin and a Barbarian, and those guys are supposed to be the tanks. The HP is what they get for losing the ability to cast like a caster. My 2 DDO Points would be to tone that down. Do what you want of course, but it does seem not awesome to me that a Full Casting FVS or Full Casting Cleric would have more base HP than a Paladin (which is supposed to be the Half Fighter Half Cleric).
P.S.: Fun Fact I learned recently, no bearing on any of this, so feel free to stop reading now. 3.5 Gives Clerics Turn Undead for free, and Damage is a feat (or ACF).
Pathfinder (Which is very very similar to 3.5, sometimes called "3.75") chooses to go the opposite, clerics get Channel Positive or Negative energy Burst for free, and need to burn a feat to gain Turn Undead.
Just something I liked.