The differences in these vinegars is the ratio of acid to fluid. Just as if you took any other acid and diluted it past a certain ratio, it wouldn't have the same effect. 5% vinegar just doesn't have enough acid to do the work. You have to have a strong enough concentrate for it to be acidic enough to work. Pickling vinegar is 10% because it has to be strong enough to break down the cells in the food you want to "cook". You can't use 5% vinegar and get a good result. 20% vinegar is stronger by ratio. If you use 20% vinegar, 1 oz. of concentrated orange oil and a drop of soap, you WILL kill those weeds. Remember it kills by burning off the greenery and eliminating photosynthesis so if the weeds have enough root system to regenerate they will, but a second application is usually enough to deplete their reserves and kill the plant. If you do it on a hot, sunny day it will accelerate the process to just a couple of hours. I hope this will help you get over your frustration. I agree, it's too darned hot to have to use a weedeater.

And yes, there is a difference between natural vinegar and synthetic, same as permethrin and pyrethrin; one is created by artificially combining chemicals to mimic the natural product, the other is created by natural processes.