Quickly:
Both systems are very different.
I drop shot for wrasse but, strangely, we discovered that deep water is the last productive place to search for them generally. You can drop shot at any reachable range. Only the actual presentation of the SP changes and, go over vertical or near vertical and, the best, most natural way to present the SP is wacky because, no matter the rod:line angle, the lure is level orientated and shakes greater wacky rigged anyway IME. Shake slack line, not a tight one. At no time should the line go tight (well, it can on cleaner ground) or you risk pulling the weight under any obstacles etc.
Carolina:
Sink and Draw ? Yea, It does work but, the takes are indirect. I:e, the weight and lure/weight are not inline.
Japanese carolina: very short link length, weight is maybe 3 " from the lure (better a floating or mobile one) for our HRF due to the fish type.
We utilise glass beads in the line up to generate sound. I think it makes a difference. Again, quick taps without actually moving the weight activate this clacking.
I mostly use a carolina 'ground based'. Weight maybe 18" away from the lure which, in the case of an xlayer will NOT be level rigged. I might do this from a beach as an example.
Basically, you JERK the weight OUT of the bottom. This, NOT the weight landing, makes the sand puff up. Shrimps etc live in the sand. They emerge at night in the shallow surf just as sandeels bury themselves at similar times. Move the weight that 18" and, the 'just offset rigged' lure, like an xlayer, flat side down and slightly banana rigged will plane UP and fall right over the sand or mud disturbance. You JERK and 'release'. Let the lure fall on a semi slack line, hold the line in thumb and forefinger and wait for a draw or pull. Push the rod forward slightly before setting the hook if using 'braid'. Mono usually has a built in timing.
If you refect on 'Jerkbait' style lure fishing, you JERK the lure down making commotion and then, the lure comes to rest in that very same commotion zone. Lure and commotion are in the same spot. Bass, drawn to it should find the lure immediately.
With a bounced jighead over sand this isn't the case. We have to consider a few aspects.
Jighead hits bottom. (sound), lure is where the sound or bottom tap is made. Great for hard bottoms where both noise and visual presence are in unison.
Use a Carolina over hard ground and the carolina weight sits where the sound emerges and the visual 'lure' is way behind. Not in unison.
Add sand or actual bottom disturbance into the eqaution and it becomes muddied.
Jig head leaves the bottom creating a 'puff' or cloud of mud/sand but.....
The lure has moved AWAY from the disturbance and is not in unison. Bass moves to the sand puff and the lure isn't there.
Carolina weight leaves bottom, throws up sand or mud puff. You jerk 12 or 18" or whatever. Your lure falls slowly over the area of disturbance.
Yes, you weight has also hit bottom away from the lure and puff of sand but the 'luring' ratio is in favour of the lure AND puff of sand plus the pressure wave created by the movement of weight, lure and bottom debris.
Loads more to it but I hope that helps and makes sense.