There are 3 weapon types: Missile, Kinetic, and Beams. Each weapon type has an opposing defense type that blocks attacks from that weapon type (point defense for missiles, armor for kinetic, and shields for beams). Each weapon type is unique in it's own way...
-Missiles have a ranged volley attack, that can be used out of regular combat to do a volley of damage against a target up to 3 hexes away.
-Kinetic weapons do the most base dmg, and get slightly more benefit from extra research.
-Beam weapons have a slightly lower construction cost, and the later game weapons that cost special resources cost slightly less special resources (which is useful since elerium, the resource needed for beams, is the hardest to mine).
All weapon types now have the same range, accuracy (80%), and rate of fire in battle.
Damage: The actual damage is now a random number between 1 and the damage shown on the weapon type. So if you have a beam weapon ship that shows 3 beam dmg, that actually means that each attack will be a random number between 1 and 3. The defenses work the same way, a random number between 1 and the max defense, but defenses also work a little different...
Defenses: The defenses block their weapon type equal to the random amount between 1 and max of that defense, but the square roots of both the other defenses are also added to the main defense, so it's a number between 1 and that max. so if you have 10 shields, and 9 of each other defense, and you're being attacked by a beam weapon, then your max defense will be 16 (10+3+3). So your actual defense will be a random number between 1 and 16 against each beam attack, blocking that much dmg from that attack. The minimum damage from any attack will still be at least 1 though. Weapon attacks are never fully blocked.
The way targeting works right now, it can be argued that smaller ships can have an advantage over larger ones, since excess dmg to smaller ships is currently wasted, and each large ship can only target 1 small ship at a time. Smaller ships generally have more item slots but less hp per logistics point compared to bigger ships, esp. after the first miniaturization tech is researched, adding +1 item slot to all ships.
Additional combat info, including info on ship roles, can be found on the official gal civ 4 wiki here: GalCiv4:Spaceship Battles - Galactic Civilizations - Official Wiki