How to Set Up a Wireless Router m Setting up a wireless home network High Speed Internet. - Verizon Home networking explained, part 2: Optimizing your Wi-Fi network
Am I correct to assume that the WAN IP / Public IP assigned to me by my ISP is at the external side of the modem
Yes, the IP assigned by your ISP is associated with the WAN (wide area network, or "external") side of your modem.
or is it on the external side of the wireless router?
No. (We know this because you have a public IP and because you provided a subnet for the network between modem and router.)
Note: It is possible your modem could be configured as a bridge, making your wireless router your gateway device, but that sort of config is incredibly rare these days when nearly all devices do DHCP and NAT.
I am guessing that the External IP of my wireless router has to be on the same subnet of the internal IP of my modem
Correct. The WAN IP of your wireless router is on the same subnet as the LAN (local area network, or "internal") IP of your modem.
In a nutshell, 192.168.100.XXX is a two-device network consisting of the LAN side of your modem and the WAN side of your wireless router.
Then on this assumption I'm leaving behind modem internal IP, and External IP of the wireless router would have to be on the same subnet of the WAN gateway which is getting a bit confusing.
Again, yes, there's a subnet between the modem and the router. There has to be, in order for traffic to flow. (You could get rid of it by bridging your wireless router; then all the devices on the subnet would be getting IPs from the modem instead but there's really no reason to and most wireless routers these days don't even do bridge mode.)
If your setup is typical, this is what's happening:
Subnet 1: Your modem is getting a public IP from your ISP. (This IP might be statically or dynamically assigned, but either way it's a public IP address.) Your modem is on a subnet; it sends traffic to the internet through its gateway IP, which belongs to the ISP.
Subnet 2: Your wireless router is getting a private IP from the modem. This causes the little subnet between modem and router.
Subnet 3: Your wireless router is also a DHCP server. Your client devices -- laptops and tablets and phones and such -- are getting private IP addresses from the wireless router. This is a different subnet than the one between the modem and router.
Your traffic is what's called "triple NAT-ed," meaning network address translation is happening three times. This is totally typical in modern home networks.
You can functionally ignore the little subnet between the modem and router, as no one ever uses those IPs but the two devices themselves, but it is important to know that it's there for troubleshooting purposes.
How to Set Up a Wireless Router m
Setting up a wireless home network High Speed Internet. - Verizon