The confusion stems from the fact that networking has evolved greatly since the ARPANET. In the past, yes, location and distance was the predominant factor in the distinction between LAN and WAN, however today, it is both blurred, and somewhat re-defined. Today, the distinction is more in terms of addressing and administration, particularly for “LAN”.
A LAN no longer needs to be in a single location. Yes, a home, school, or company-network is considered a LAN, but the term also applies to ISPs. That is, your ISP may provide Internet access to thousands of houses across a large city, and it is still considered a LAN (for example, consider warnings of how someone using the same ISP may be able to sniff your traffic because they are on the same network). In this case, the addresses of the systems on the network are confide to the IPs that the ISP owns and the network is administered by the same entity (the ISP).
A WAN on the other hand is usually defined more closely to what it was in the past: a disparate networks connected to each other. In this regard, your home-network connected to my home-network forms a WAN, even if they are both on the same ISP. In this case, each sub-network in the WAN is administered by a different entity (you and me), and likely has different addressing (your router may use different addresses, network masks, etc. than mine).
Another definition for a WAN that falls in line with what it used to be does in fact use the location. For example, a company can have a LAN in their office building, but when it connects to their LAN in another building in another city/country, it forms a WAN.
It’s sort of a matter of perspective; two small LANs form a small WAN, which itself is a LAN that connects to other small LANs which form a larger WAN, and so on.
Another distinction for LAN and WAN that is easy to remember is the makeup of the networks. A LAN is usually just individual systems/devices connected to each other, while a WAN is usually networks connected to each other. That is, you don’t usually have a sub-network in a LAN, and you don’t usually have a single computer attached to a WAN all by itself.
Also, the networking hardware usually plays a role in the distinction, for example routers in LANs and switches in WANs; CAT5 cables and little wireless antennae for LANs and giant under-sea cables and satellites in orbit for WANs.