The difference between wired and wireless computer connections lies predominantly in the speed and stability of the connection. A wired connection generally has a faster, more stable connection when it is compared to the wireless type.
Wireless, also called Wi-Fi, has some coverage issues as well. The total number of users on a wireless connection, the wireless access point, the transmission power of the card, sources of interference and the total traffic can determine the strength and speed of a Wi-Fi connection.
Security can also be an issue when using Wi-Fi. The security of a wireless connection is only as strong as the level of security encryption in use.