LANs and WANs are types of computer networks. There are no specific definitions between the two however there is agreement on generalities.
LANs are Local Area Networks. They are networks that are in a small area such as in a business, home or similar. Your network at home and at work is considered a LAN. They are in a small geographic are. The network within your business is considered a LAN. However, if your company covers a large area for instance is in several cities or states or international then usually it is in a single city. However, in some cases if it has been setup as all stations in it operate as if near each other it may extend across cities.
WANs are Wide Area Networks. They are networks that cover a large a\geographic area and are made up of several LANs. All of the technical colleges in Georgia make a WAN, however each college would be considered a LAN although in some cases each campus may be a LAN.
Your network in your home is a LAN and it connects to a WAN that is your Internet Service Provider such as Comcast, Northland, EPB and others. However, their network for a specific area may be considered by some as a WAN or LAN depending f seen as covering a large area. There is no strict definition of an area for either. In a high rise building a LAN may be one floor and a WAN on all the floors.
LANs and WANs are general terms but could be considered different by different people as what they consider local or wide area.