(G) = Gimballed, will auto-aim if the target is in front of you. Though since Beta 1 they seem pretty buggy for many users and just oscillate around the target.
(T) = Turreted, will auto-aim and fire on targets in all directions apart from going through your own ship of course

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Pulse laser = single pulse of damage.
Beam laser = hold on target to do damage while you hold.
Burst laser = essentially a pulse that shoots three pulses in quick succession. Uses much more heat & power however.
Cannon = a cannon, shoots a single projectile like a cannon ball. Does heavy damage to hull.
Multi Cannon = machine guns, shoots rapid fire small projectiles.
Rail Gun = Takes about 2 seconds to fire after holding the fire button and will fire a large beam doing heavy damage. This is considered an energy weapon, though technically a 'rail gun' should shoot a large projectile at extreme velocity.
Missiles = heat seeking missiles.
Energy weapons hit shields harder, Projectile weapons damage hull better.
You can mix match weapons however you like on hard points. It is usually best to keep energy weapons and project weapons on their own fire button as they require different ways of aiming to hit your target. Projectile weapons require you to lead your target, energy weapons require your cross-hairs to be on target. Missiles require a lock.