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.