Is there a rigorous difference between a WAN and a LAN?
Historically, very different technologies were used for WAN and LAN in the past decades. Today, it's all becoming Ethernet that started out as a LAN-only technology, but has significantly increased its link reach, from 500m to 100 km. Accordingly, it covers LAN, MAN and WAN today (plus shorter reaches).
So, all that differs now is the physical-layer 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. Single-mode fiber within a data center is rather common.
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. A firewall is required in between, filtering out unwanted traffic.
All in all, there are certainly rigorous differences in specific situations, but those depend.