Two routers connected with a serial cable are just that - two routers connected with a serial cable.
Until you tell us about the physical layout of your hypothetical network, we can't use terms like LAN / WAN / etc...
Note how these terms are all tied to the physical configuration and size of a network. We don't use these terms to describe logical configuration (i.e: "two routers connected with a serial cable")
Additionally, a "serial cable" implies RS-232 (possibly RS-422), and isn't really considered to be "networking" within the in modern definition - it's used all over the place for configuration and direct interfacing.
In some industries RS-485 is used for point to multi-point networking (with a specific master)... but if you're talking about this, then you're not talking about IP / Routing / X Area Networks.
I suspect you don't mean "serial cable" - i.e: DE-9 (aka DB-9):
Instead, you probably mean, "network cable" - i.e: CAT5 / CAT5e / CAT6, terminated with RJ-45 connectors:
With your addition of a diagram, we can now establish that you probably do indeed mean "network cable". In this case, as mentioned above, the physical / geographic size of the network determines what it is called (LAN / MAN / WAN / etc...).
- If Network A (
172.16.0.0/16) and Network B (
192.168.0.0/24) are in the same physical building, then it's probably still referred to as a LAN. Just with two segments that have routing between them. Arguably it could be considered two LANs with routed access to each other.
- If Network A and Network B are in two separate buildings in the same neighbourhood, then it's possible that it could be considered a MAN.
- If Network A and Network B are in two separate buildings in two separate cities, then they could be considered a WAN.
The whole network is considered for this terminology - not just the link between the routers.
It's highly likely that Network A is a LAN, and Network B is a LAN.
If you want to know what the "red link" is called, then one of these could probably fit:
- Patch cable
- Network cable
- Fiber optic cable
- Leased Line
To offer an alternate explanation: "Teacher at school was referring to it as WAN connection"... he is probably familiar with consumer (home) routers, which mark "the port that connects to the internet" with the label "WAN". It doesn't mean that the link (and only the link) is a WAN, but rather that the consumer router connects to the WAN (i.e: Internet) via this port.
To poke further issues at your question and setup,
188.8.131.52/4 is reserved for multicast addressing. If you are using this for any other purpose, then you may (will) run into odd / unexpected behaviour.