ah the memories that brings back
The ADS II and the ADS III were Garrett's attempted "answer" to the Whites 6000d's. But in my opinion, the 6000d was better (deeper seeking, when matched coil-size per coil-size relative). Still though, a good machine for its time. It dates to around 1982, if my memory serves me right (maybe as early as 1981?). It was a motion machine, and a hair-slower motion needed than the 6000's, it seemed. The 4", 8", and 10" coils would be for regular coin hunting. Smaller coil for junky sites (ghost-townsy type iron ridden sites, or under bleachers, etc...). The 10" would give the most depth in regular coin/turf type hunting, albeit with more masking than the smaller coils.
Not sure about the 15" coil. But no doubt the logic would follow the same as ANY larger coil on a standard coin machine: More depth. The larger the coil, the deeper you go. However, you hit a "point of dimishing returns" on coin sized targets, where .... eventually ..... you only get larger objects deeper, not coin-sized objects deeper. Or perhaps it was used to get more coverage swath per sweep, even if not getting coin-sized objects deeper. Or I suppose the logic would be that if you were hunting jar sized items at depth, you might want to get that 15" coil on. But personally, if I was going to go out with the sole objective of finding "jar sized objects", I would simply elect to use the blood-hound feature, not larger-standard coils.
The blood-hound device turned it into a 2-box unit. Not sure how effective it was on that (as compared to, say .... a TM 808 ), as I never used one of those attachments on the ADS II I had.. But in general, a 2-box unit allows the detector to *only* be able to sound off on soda can sized objects or larger. You simply won't hear small things like individual nails, coins, etc.... So it's the best way if your objective is solely large objects (like cache hunting). The depth on the 2-box units I've used (the tm-808 ) is about ~2 or 3 ft. on a soda can or mason-jar sized object. 3 or 4 ft. on a tool box sized item. 4 or 5 ft. on a toaster oven sized item, etc.... So too can a standard detector (esp. with a 15" coil) probably get those same depths. But the advantage of the 2-box is you're simply not bothered by all the nuisance small stuff, to be having to endlessly do the guessing game of small versus large.
As for what each control does, well..... that's a different subject, and I've gotten too lengthy thus far here
Will let someone else take a crack at that, unless you had a specific question. I see from the pix that you have the instruction manual, so why not just read it ?