A LAN (Local Area Network) may appear faster to you because you're communicating with computers that are in the same office/building as you, very physically close, and the data won't have far to travel.
A WAN (Wide Area Network) is a bunch of building-based LANs, all connected together. The 'pipes' connecting the LANs together will be 'wider' (faster) but as the data will have farther to go, it may actually feel slower.
So - a WAN has faster pipes, but performance on a LAN may give you faster results.
Local area network is more fast than WAN in most of the cases as WAN includes cable and satellite channel but still with the fast growing technology and fast broadband, it looks they are very much close.