What's the difference between a wireless adapter vs. wireless router?
For example: I've heard some mobile devices that have a support for WiFi. Can they work as wireless adapter or router?
The most used version of a wireless adapter is a device that you plug into a USB port of a computer that doesn't have wireless capability if you want wireless capability (see the following picture).
A wireless router is something that provides a wireless LAN. Sometimes a wireless router will also act as a modem. Some smart phones can act as "hot spots". This is basically like having a mobile wireless router/modem any where you have cellular service. This normally costs extra though.
For more information, please see the following links:
A wireless (wifi) adapter will be a device that can add wireless functionality to something - for example a wireless USB 'dongle' added to a laptop that has no built in wireless functionality of its own:
A wireless router acts as a 'base station' for wireless (wifi) devices, connecting (routing) them to another network. The unit below is a wireless router and can interconnect wireless devices + 4 wired devices and has a WAN connection to, say, a broadband or cable modem, providing a link to the Internet.
A mobile device - such as a phone - with wireless functionality has an adapter built-in. In some cases as well as providing wireless connectivity for the mobile device they can be configured to work the other way round and allow other devices to connect to the phone wirelessly and then onward to the Internet via the phone company's data service - in effect acting as a wireless router or 'hotspot'. The picture below shows an Android phone being put into hotspot mode:
Well, a wireless adaptor is allows a computer to get on a wireless network. A wireless router is a router with wireless capabilities - in addition to being, well, wireless, it also handles routing, DHCP and other things.
all wireless adaptors can work ad hoc, (or peer to peer)
SOME wireless adaptors have 'AP mode' which allows them to act as an access point or router.
MOST mobile devices with wireless support act as if they had a adaptor, as opposed to acting as a router - the exceptions are things like mifi.