Note that the process involves negotiations going along with documentation. Rarely do real estate transactions occur with a handshake followed by the paperwork. Most often the paperwork forms the offer and signing concludes the contract. What is most common in counteroffers is a change in price. Even if the parties agree on every other issue and term, no contract can be formed because of this fundamental disagreement.
Terms are also important.
It can also contain mortgage contingency clauses and other modifications that are routinely agreed to in an otherwise handshake deal. Often there is a tradeoff between terms and price. One party gets their price while the other gets more favorable terms. In most parts of the country, real estate agents will prepare offers and counteroffers. In the past they would actually write out much of the text of the offer in longhand and then have everyone sign.