The sects basically have a basic change that impacts everything you do, and then a bonus effect that impacts your Aspected spells.
Diurnal sect is regen stance. It gives you a base 5% increase to cast speed, and then adds a regen to your Aspected Benefic (single target heal) and Aspected Helios (AOE heal) spells. These you use in addition to normal Benefic and normal Helios, not instead of. Think Medica and Medica II.
Nocturnal sect is shield stance. It makes all of your heals 5% stronger, and adds a shield to Aspected Benefic and Aspected Helios.
You cannot change stances in combat. Diurnal is generally preferred--the MP return is better than Nocturnal. Diurnal regen also stacks with WHM regen. If you have two AST, one should go in each stance as AST regens/shields do not stack. Neither do cards, so you have to be careful about not overwriting cards in a double-AST situation.