Armor, Shields, and Barriers are all "Defenses" that protect enemy (or Shepard's) healthbars from harm.
For Shepard personally, its largely irrelevant. Only two of the six possible Shepards have barriers (Vanguard / Adept), and none of the six have armor. For Shepard, Barriers and Shields differ only in color (purple vs. blue), as any armor piece that improves shields will likewise improve barriers.
Shepard cannot get armor at all; the Fortification power, despite claiming to be armor, is really a damage reduction, like Tech Armor (which, despite the name, is actually advanced shield tech).
For enemies, it matters a little more.
Armor
Indicated by a yellow health bar. Vulnerable to fire attacks, like Incinerate, and damaging biotic attacks like Warp and Reave.
Common to Cerberus Robots, Environmental obstacles, and reaper forces.
Slow firing weapons like Sniper Rifles, Heavy Pistols, and Shotguns tend to do better damage to armor.
Finally, Armor can be "weakened" by freeze effects and "penetrated" by weapon mods, or Armor Piercing Ammo. Incendiary Ammo, Warp Ammo or Armor Piercing Ammo, will all do additional damage to armor.
Barriers
Indicated by a purple health bar. Vulnerable to damaging biotic attacks like Warp and Reave, and by Concussive Shot.
Common to biotic users.
Fast firing weapons like SMGs and Assault Rifles do better damage to barriers.
Barriers also take additional damage from Warp or Disruptor ammo.
Shields
Indicated by a cyan health bar. Vulnerable to tech attacks like Overload and Sabotage.
Common to Geth, Cerberus, and certain Reaper forces.
Fast firing weapons like SMGs and Assault Rifles do better damage to Shields.
Shields take additional damage from Disruptor ammo.
Other than the fact that drones can move and turrets don't as Raven pointed out, here are the other major differences:
- The base drone damage is higher 40 to 25 and the drone gets more potential damage/shield upgrades.
- The turret can potentially get an ammo effect (AP or cryo) and a flamethrower (high close up dps)
- The drone can get an explosive effect when it dies and chain lightning (stun multiple targets)
The combat drone is offensively oriented and seems to be typically way better at distracting large targets than the turret as it can, and will, move in close and start zapping away. The turret is a lot more defensively oriented, designed to hold one spot on the battlefield or protect your flanks, etc.
Best Answer
The difference is largely what it sounds like, the Combat Drone does more damage than the Defense Drone, but it offers less utility and survivability, and is less effective at drawing fire away from you.
The Combat Drone is focused on dealing damage to the enemy, and it's upgrades reinforce this by improving it's damage output directly. The Combat Drone can also be deployed at fairly long ranges, allowing it to be used offensively. However, be careful placing a Combat Drone out under fire - they can be destroyed, and without upgrades, are fairly fragile.
By contrast, the Defense Drone will stay close to Tali, and only attack targets that come into range. It's damage output is fairly low, but it's attacks will stun opponents, and upgrades will increase its range and utility, allowing it to stun more targets, more often, at longer ranges, and adding the potential for a knockdown. Most importantly, the Defense Drone cannot be killed, making it an excellent 'passive' source of extra damage if you aren't interested in managing and actively targetting power use.
TL;DR: Use a Combat Drone to kill things before they reach you. Use a Defense Drone to keep them busy so you can kill them if they get too close.