I agree with all of the other answers that have been given. The main thing is that in the US real estate law is governed by state law not national law. Each state has its own rules. In Arkansas, for example, the closing occurs when the buyer and seller sign all of the papers involved in the sale. This occurs at a title company which has done a title search on the property and will provide title insurance, as well as facilitate the actual sale (transfer of funds, etc.).
In other states, there are other rules. For example, as mentioned in other answers, there are other procedures and timelines. Also in some states, closings are handled by attorneys.
Thus wherever you are interested in purchasing a home, it is very important to get a buyer agent who can represent your interests and explain the process in that state to you. Normally there is no extra cost to you to have a buyer agent. The seller pays his "listing" agent a commission which is divided between the listing agent and the buyer agent . When the listing agent puts the listing into the MLS (Multiple Listing Service), the listing agent indicates how much of the commission will be given to the agent who actually sells the home.
The Multiple Listing Service (MLS) is a database of all of the listings in a particular area whicjhare currently on the market. National Association of Realtors rules permit individual agents to show all of these listings on their personal websites. Normally if a home becomes unavailable (i.e. goes under contract or is withdrawn, for example), the listing disappears from those websites.
Hope this helps in understanding the system here. If you have further questions, ask your buyer agent.