So I have two IP addresses - one is on my network settings and is 192.168.0.X. Another one - I checked this address online - is 108.X.X.X. What's the difference between these two IP addresses? Does it have something to do with local vs internet IP addresses? Can someone please explain these two concepts?
The 108.x.x.x is the IP address that the rest of the internet sees. The 192.168.0.x is the internal IP assigned to a particular host in your own network, typically from your router.
Lets say you have 5 computers all on one router. When they connect to the internet, they all look like 108.x.x.x.
When the server responds, and returns the message to the router, the router determines which internal IP that the message was intended for. This is called Network address translation
192.168.** is an IP assigned to the machine from a Router.
108.*** is an external IP.
You are correct, one is your local IP address(assigned to you by your router) and one is your public Internet IP address (Actually the IP Address of your router).
You internet service provider(ISP) assigns your router the 108.x.x.x IP address and that is how all computers connected (either wired or wirelessly) to your router connect to the internet. All of your traffic goes through your router before going to the internet and vice versa. Your router assigns all the devices connected to it an internal IP address(188.8.131.52.x) and handles routing all traffic to the computer it needs to go to (which is where it gets its name from).
192.168.x.x is an IP address used on a private network. There are 3 reserved ranges of addresses for private networks, and this is one of them (there are other reserved ranges for other purposes). These IP addresses are meant not to be routed directly outside a local network (e.g. within the home/institution).
108.x.x.x would be a public IP address, routable from anywhere on the public internet.
Most modern routers that are in between the internet and a private network can convert the traffic from an private IP address (and vice versa) using Network Address Translation (NAT). Other methods for being able to access machines outside a private network include using a proxy server with an interface on both networks.
Public IP address is an unique address assigned by Internet Service Provider.
Private IP addresses are provided by network devices, such as routers, using network address translation. Private IP addresses can only be guaranteed unique to an internal network.
Public address is like house(assume apartment) number provided by local government. Private address is like flat number which is assigned by apartment in-charge.