The big difference is when you are inside your local network behind the router, or at work behind a firewall simple accessing the wan-ip won't reach your machine, unless you do port-forwarding (which isn't always straightforward or even possible.)
Ngrok solves this problem by being in the middle, both your machine and a person visiting alias.ngrok.com are connecting to ngrok, ngrok just passes the data along.
What this service however is good for is to have a dns address that always points to your local machine or your home network if your ISP doesn't provide you with a static ip (thus your ip changes every so often).
That pretty much is (or was, not sure how most games currently handle networking) the main frustration of setting up a game server at home for your friends at their homes.
One solution back then was to use Hamachi to create a "virtual lan network". Btw for some use-cases you could even use "ssh -L <local port>:<remote computer>:<remote port> <user>@<remote ip>" with a server, and certainly nowadays you can get a vps at 12$/year (nothing fancy, but good enough for tunnelling ports).