Years ago I helped a friend buy a new car. I gathered all the facts I could on the car and searched around at prices and option packages before I made the move on one particular dealership that had the car the guy wanted. Of course the salesman started off a little below his own sticker price to make it look like we were getting a deal.
After haggling with the guy for a long time and him doing that back and forth schtick with having to ask his manager and me threatening to walk out (The guy I was with wanted to grab the deal at one point) I finally exhausted the salesman enough that he brought out the invoice to prove they were only going to make $500 on the car and I said OK.
A lot of our past negotiations were a little different then they are today. But you are "somewhat" right. Let's say the Company in their minds for example is willing to tack on 500 Million to their Labor Cost expenses in these talks. Do you think they walk in the door and tell us that they're willing to do that? Of course not. The first aim of course is to try to flim flam and get a cost neutral deal. Hell long term even a cost savings if we had morons in there (We don't)
So over time the back and forth commences to get to that (unknown) bar they have in their minds. Other factors can also play in getting to that bar. Timelines they want or need it done by for either investor security, loan agreements, a POR, or Executive performance bonuses, or even something they feel they can work with.
The only time how you word it comes into play is if you are in concessionary bargaining talks (Where costs need to be cut either through BK or the fear of BK, "What NYer went through) or they throw a number out so large that you bulge your eyes out of your head and they tell you to put the pieces together to make it fit.
Otherwise it's almost like a game of cat and mouse trying to figure out how much they're willing to sell that car to you for, before saying they're done with you and let you really walk out of that dealership.
Hope this helps clear it up for you a little?