The difference is pretty self-explanatory really, although the result can often appear similar.
In Defend mode, your NPC will only attack targets that fire on you.
If you're flying around a CZ, and no enemy fires at you, your SLF jockey will just carry on flying in formation.
In EAW mode, your NPC will attack any target from a hostile group.
In a CZ, once you pick a side your SLF jockey will engage any ship from the hostile faction as they see fit.
The reason they can end up yielding similar results is because of the way NPC AI works.
In Defend mode, If a ship attacks you and then decides to run away (usually because it's either heavily damaged or crippled), your NPC will attack it, and continue attacking it, even if it's no longer a priority threat and different ships have subsequently attacked you.
In EAW mode, your NPC might choose a target to attack and that ship might decide to run away and your NPC will continue attacking it regardless of how far away from you it gets.
Added to which, with either of the above things going on, you might also decide to engage a ship that takes you in a direction away from your SLF.
In any of these situations, it can end up looking like your SLF jockey isn't really doing his/her job but they are - in accordance with the AI NPCs in ED employ.
The whole thing is the result of the way NPC AIs decide to "pair off" in combat.
NPCs, including your SLF jockey, will pick another ship to attack and then keep at it until something explodes or, at least, they take sufficient damage to make them retreat.
In Defend mode, particularly, this can lead to your NPC relentlessly attacking a ship that's decided to run away even if it's no longer a threat and other ships are now attacking you.
Personally, I find the best way to work with an SLF is for you, in the mothership, to fly "support" for your SLF.
Keep an eye on where it is and help destroy it's targets if possible.
That way, your NPC's AI will reset once the target is destroyed and it'll go back to acting predictably.
The only time I ignore this is if there are high-value targets around.
When that happens, I'll go after them and my SLF jockey is on her own until I've exploded whatever I'm shooting at.