Forums and chat are two of the most common ways that people communicate online. They have similarities but there are also some pretty big differences. Understanding these differences is important to allow you to decide which of these options is best for you. That being said the vast majority of people find forums to be the preferable option.
The big difference between a chat room and a forum is that chats occur in real time. In order to chat with somebody you both have to be online at the same time, it works like a conversation that goes back and forth. A forum on the other hand is more like a bulletin board, you can post your message and then people can come by and read it at a time that is convenient for them. They can also respond at a different time as well. This greatly increases the number of people who can take part in the conversation.
The other big difference between chat and forums is that forums are almost always moderated. That means that there are going to be rules about what can and can't be posted on the forum and you break those rules you will have your post taken down and possibly be banned. With chat since it is happening in real time it is impossible to moderate what is being said. You may be banned if you repeatedly break the rules but whatever you choose to say during the chat will be available for the other chatters to see.
Forums also tend to archive the posts that are made on the site. That means that they will be there for years to come. In addition the content of the forum is usually crawled by the search engines so it will often be indexed. That means that if somebody does a search for something that has been discussed on the forum it may well show up in the search results. This is not the case with chat which usually disappears as soon as the chat session has come to an end. The result is that a lot more people will see what has been said in the forum.
One of the other differences between a chat room and a forum is that the forum tends to be much more of a community. At a forum people have to register in order to participate and things like post count are kept track of, therefore they can be involved for years. With chat on the other hand people tend to come and go much more frequently. The result is that people don't get nearly as well known as they do on forums. At a forum you may spend years building up a reputation by participating in discussions, this does not usually happen with chat rooms.