Ok, well I'll do my best to explain to you the different functions of each, I'll try to use the info from the NRaas site.
Overwatch is the overseer, it just stands on guard and overlooks the file for issues you may have. For instance, NRaas says that on the startup of a save file, Overwatch does (I'll edit some of these to make them more understandable, as well as shorten the list - this is not ALL it does, this is only a few of the things it watches for on startup of your file) :
>The aging is disabled on the Grim Reaper, Deer, and Raccoon sims
>Sims in recursive postures are reset (Sims in areas that are considered "stuck" or glitched)
>Newspaper articles that reference a lot that no longer exists in the game are removed
>Bonehilda coffins that reference a sim that no longer exists are repaired (A common issue for Bonehilda is she'll sometimes disappear and stop coming out when you call, this fixes that minor glitch and prevents other glitches).
>Sims with corrupt skill lists are repaired
>Broom Riding skills that reference a lot that no longer exists in the game are repaired
>Sims who reference a missing career outfit index are repaired
>Careers with corrupt coworker lists are repaired
>Careers referencing a career location that no longer exists in the game are repaired or ended
>Sims exceeding the maximum celebrity level are corrected
>Sims missing their cell phone, or have multiple cell phones in their inventory are corrected
>Collecting skills that are missing GlowBugData, MushroomData, HarvestData fields are repaired
>Collecting skills are reconciled with the Gardening skill to ensure that the information displayed in the Collection Journal is complete
>Lots with corrupt SavedData entries are repaired
>Occult sims which do not have the proper hidden traits or occult states are repaired
>Corrupt opportunity histories are repaired
>The CAS pattern list is reprocessed, and any unreadable patterns are logged to file
>Long-term relationships assigned to sims that no longer exist in the game are purged (Relationship Panel Cleanup)
>Show stages with corrupt objects assigned to them are repaired (such as Venues from Showtime)
>Sims whose "Household" field does not match the household they are actually assigned to are repaired
>Duplicate alarms assigned to process the exact same task, at the exact same time, are purged
>Zombie Spawn alarms found running on load-up after ended
>Sims who have traits assigned that no longer exist in the game are repaired
>The Consignment system is cleared of "negative day" objects and sales objects that cannot be properly listed
>Counters lacking proper PetSurfaceComponent entries are repaired
>Imaginary Dolls lacking their associated service sim are repaired
>Fix for cumulative skill gain issues caused by positive moods
>Fix for corrupt rock band skills
>Fix for broken mounted fish objects
In general, Overwatch also checks for stuck stuff every Sim Hour and every four Sim hours it double checks everyone in town to make sure they don't need to age up (or if they are due to age up at all).
This mod in general makes sure that your Werewolves age up on time, that Stuck Sims always get reset at 3 am every Sim day, and that Sims in general are less buggy. Overwatch is basically for Sims and the things Sims are interacting with at time of issue.
Errortrap handles corruption and error logs. When an item gets corrupted (it can be anything) it's kind of like a virus. It can spread easily, so Errortrap scans for those issues and cuts them off to prevent it from spreading. Things this usually pertains to are items that get bugged, like things that get stuck in your Sims inventory, where as Overwatch is more for when your Sim goes running to collect a gem and finds himself/herself in an unroutable position and cannot move.
Here's a great example of overwatch at work: whenever I adopt children from the Service menu, the Social Services woman will arrive, but the kid will not. The portrait will show up on the side and join the rest of the family, but when I click to find out where she is, it's usually not on the map. Now, I can reset her myself because I'm aware of the situation, but otherwise she'd be stuck there causing massive errorlogs to bog down my game. Overwatch, after a few Sim minutes of realizing that she won't walk out of the unroutable area she's in, will reset her automatically to the house.
Errortrap will find corruption and cut it off at the source. Easiest way to say it is, if your Sim goes to Graduation at the City Hall, but suddenly Sims decided to put a protest there as well as a pregnant Sim giving birth because she couldn't get to the hospital (true story, did happen) your Sim could wind up interacting with the City Hall as it bugs out, thus causing Corruption. This is where Errortrap comes in. Normally it would cut off the source of the bug, but at this point it's already interacted with my Sims so it lets me know that there are some massive errorlogs (by giving you notices where you normally receive information about leveling up in skills/career/etc). I reset the whole town, then reset my Sims lot and that took care of the issue before it became a massive problem.
Overwatch fixes, Errortrap prevents.
Simplest explanation.