The confusion is the difference between best practices and general practice. Don't worry about it. When discussing electrical systems you can get caught up in the language and examples and lexicon. I read a great thread on Expedition Forums about this term voltage drop. Three very intelligent and professional engineer types. It would have gotten killed on this forum as it got very heated. Each was looking at complex systems, far more than here and coming at the solutions from different directions. It was like watching Bob, from Bob's solar page debate with someone as smart as Sternwake here and another top notch professional from the marine industry.
First and foremost, wire is cheap. I know it doesn't look that way now. But after everything is in and built and happy day camping, saving a a dime or two will cost you a C note or three. If/when you have an issue. House wire is designed for foundation houses and those only move in California. Solid wires break when they wiggle and they can break quickly with the right frequency wiggle. Jiggly, Wiggly Club=Good, Van/RV= Not Good. Yes some RV's do it. Because it is cheaper and they won't have to fix it. You will.
Second. Think of wire like a water hose. From power BUCKET you have high pressure low volume or Low pressure high volume. Pressure is voltage and volume is amperage. Each of these hoses have to be different is sizes. High pressure low volume smaller and low pressure high volume larger. 120 is high pressure and 12 volt is low pressure. I hope that helps.
Stranded copper wire is the best and will last the life of your truck/rig. Read, done right, you will only do it and spend money on it one time.
The links John posted are good for cheap know quality wire. You can go the Amazon route and save some bucks but you really don't know what your getting from bulk international distributors and for most builds the savings is negligible. This is from a risk/reward viewpoint.
The BlueSea marine website has all sorts of calculators for sizing wire. Sizing wire is important. Failure in this area will start fires, smoke, and kill you. No dramatic sparks and jiggling electrocution. Just a wire that gets hot and smolders, doesn't pull enough current to trip a breaker, and gasses you with toxic materials as you dream.
Grounding. Grounding back is a good idea if anything on the circuits have a speaker. The differences in resistance can introduce a hum, or ground loop. This ground loop is like a ghost and it can effect all sorts of equipment you may plug into the build once it is done. This happens when the measured Ohms of resistance have a difference between the battery ground and circuit ground. Usually it has to be a significant difference. But Usually sucks as a word for design application. Upgrading factory grounds are good. Like a yard of cable (big wire 1 gauge). Then ten feet of four gauge from your circuit ground to the same ground bolt the battery uses. Not an expensive outlay. Personally I use the same gauge cable from the circuit that I used on the battery but this is unnecessary and probably stupid.
Everything running on 12 volt should be checked on the wire size calculator. So other than your inverter find the biggest gauge wire you'll need. Buy two spools of stranded marine grade (red and Black) as it is cheaper in bulk and use that gauge wire for everything 12 volt. If you need to add an extra cigarette plug for the new ARB later you'll be fine. If you use different sizes then you have to remember find, tap and... PITA!!!
120v should be limited in our types of builds and if you have left over 12 volt wire going bigger to an outlet is not a problem. The only issue will be the new style of receptacles that have cut and push connections. Not good for an RV but probably the reason the guy said 12/2. Without seeing the bunny it is difficult to get on the same page to cook it, right? Make sure the Battery to the inverter connection CABLES are oversized. It should be as short a distance as you can design so no big expense. If you change your batteries later you won't have to replace these cables. Not to confuse you but when Lithium gets cheap and Hybrid inverters do as well you can leave the original cables you bought and just upgrade the other stuff. So if it calls for twenty inches of 1 gauge cable put in 3 gauge, the difference in cost between 1 and 3 for twenty inches is nothing. Then later if you upgrade a little Honda 1000 plugged into your shore power will let you run the big A/C (with a soft start) as the Hybrid Inverter can switch and pull current from the battery bank and help out the little red Honda until it cycles off the compressor and then charge the batteries. In an oversimplified example. But I don't want to get yelled at for telling someone what to do by just saying spend 29 bucks on 3 gauge instead of 19 bucks on 1 gauge.
If you are confused that is fine. This stuff does get close to rocket science. I am trying to keep it lite so don't think I am being condescending. I've recently pissed off a couple of sensitive types so just being careful. If you need more help or specific help ask away here or PM and I will help you. I will also show you the models and certification standards and links as I have the websites saved as I went back and forth for two years designing what I needed.