Wi-Fi is the implementation of Wireless LAN. Wireless LAN describes the broader concept of wireless networked communications between machines. Wi-Fi is a trademark that can be used on devices that meet the 802.11 standards. Wi-Fi is used by a variety of devices to allow them to connect to wireless networks and the Internet.
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Wireless LAN or WLAN refers to Wireless Local Access Network. This is a somewhat broad term in that it describes wireless networks of machines through several means. One type of WLAN can be peer to peer, which is basically two machines setup to communicate directly with one another. Another form of WLAN is sometimes called infrastructure mode. This is the most common type of WLAN and involves two or more computers communicating through a bridge or or access point. This latter type is typically used for wireless Internet access using a wireless router.
Wi-Fi is a trademark of the Wi-Fi Alliance an organization that sets standards for Wi-Fi and certifies devices. Wi-Fi is a widely used standard and as such Wi-Fi devices can be used across the world without difficulty. Wi-Fi, basically, describes the implementation of WLAN. Wi-Fi is a technology and set of standards that allows for the implementation of WLANs.
In practical terms there really isn't a difference between WLAN and Wi-Fi, because Wi-Fi is WLAN. WLAN is a broader concept but Wi-Fi is so widespread in its use that it is effectively the only technology for WLAN in use. Wi-Fi itself is broad as it represents a set of standards for technology for accessing WLANs but isn't an explicit product or service offered by a single company. Multiple companies are associated with the Wi-Fi Alliance and set the standards. Wi-Fi is separate from certain other wireless networking technologies worth noting.
Cellular phone data networks are neither WLAN nor Wi-Fi. WLAN refers to networks covering a limited area and number of devices. Cellular phone data networks are Wide Area Networks (WAN), meaning they cover a broad area and a large number of devices in that area. Wi-Fi offers data advantages over cellular data networks, because Wi-Fi is a more broadly used and higher bandwidth delivery of wireless access. There are a broad range of cellular data networks from EVDO and GPRS to LTE. These all interact with different devices without any crossover limiting access to only particular devices for each network. In contrast, Wi-Fi is used the same all over the world and a Wi-Fi device from one country will easily access a Wi-Fi WLAN in another.
Bluetooth differs from Wi-Fi and WLAN in that it is designed to encourage specific interactions through devices that are communicating directly with one another. This is called a Wireless Personal Area Network (WPAN) and differs from WLAN, because it is designed to wirelessly unite the use of otherwise incompatible devices. While one could use Bluetooth for internet access through an internet access point broadcasting a Bluetooth signal, Wi-Fi offers the advantage of more network range and potentially higher speeds of data transfer.
As shown there are several types of wireless networks that differ from Wi-Fi. WLAN is not one of them as Wi-Fi is essentially the practical application of WLAN. Wi-Fi offers advantages over other wireless technologies that can offer some of the same things as WLAN and Wi-Fi but in a more limited capacity.