Is there a rigorous difference between a WAN and a LAN?
Technically, different technologies were used for WAN and LAN in the past decades. Today, it's all becoming Ethernet that started out as a LAN technology only, but significantly increases its reach (from 500m to 100 km). So, all that differs now is the PHY variant - LAN uses twisted pair and multi-mode fiber, WAN uses single-mode fiber (low-end WAN also uses voice-grade twisted pair). But of course you can use any suitable PHY variant for either LAN or WAN as required.
Logically, different addressing schemes are used for IPv4: private LAN vs. public WAN, requiring translation in between (NAT/NAPT). For IPv6, different schemes also exist (link-local, site-local, public), but they're used in an overlapping fashion, without need for translation.
Security-wise, LAN usually means trusted and WAN means untrusted. This commands a firewall in between, filtering out unwanted traffic.