In computer programming, asynchronous (from Greek meaning “not at the same time”) pertains to processes that proceed independently of each other.
A browser is an application program that provides a way to look at and interact with all the information on the Internet. The word “browser” seems to have originated prior to the Internet as a generic term for user interfaces that let you browse text files online.
On the Internet, chat or chatting is talking to other people who are using the Internet at the same time you are. Asynchronous communication is not considered chat.
A discussion board is a general term for any online “bulletin board” where you can leave messages and receive responses. You can also just read the board. Bulletin board services were invented for this purpose (as well as to allow for the exchange of uploaded/downloaded files). This is where the on-line course discussion takes place.
An ISP (Internet Service Provider) is a company that provides access to the Internet and other related services.