Yes, there are lots of people that tell there broker “I wanna sell this share at this price” and then there is an open sell order in the market waiting for a buyer to accept it.
How these trades take place on exchange is possibly simpler to understand if you ever traded microcaps that are like never traded. If you put in a “best price” or (whatever they call it in English) order on a share like that you will be royaly screwed.
Instead there will be open buy order and open sell orders in the market and a spread between them that can sometimes be huge for shares that aren’t traded much. Sellers and Buyers advertise there willingness to do business this way and then if they really wanna conclude a transaction somewhere in the middle of that spread they will modify there orders gradually to move closer to the buyer/sellers respectivly.
For the larger exhances and private trading you don’t need to bother with this because the are traded by so many people there is no spread between buying and selling. Orders constantly come in from booth sides at the same price. However not necessarly as many buy orders as sell orders at the current price so when all the demand or supply doesn’t fill the share will jump a cent up or down to fill some previous limit order there.