How to join a LAN world on Minecraft without being on the same internet? [duplicate]

LAN means Local Area Network. This means any device on your local network (or, as you said, "the same internet").

WAN means Wide Area Network. This means any device not on your local network.

You are looking to set up a WAN server, which you can find steps to set up on the Minecraft Website. But to do this you not only have to set up the server, but also you have to port forward, which can be a hassle.

If you don't want to set up a WAN server, you can still use special VPN services to help, such as LogMeIn Hamachi.

_{I believe that since I included LogMeIn's product in my answer, I have to announce that I am not affiliated in any way with LogMeIn}

Yes, but it is difficult. Once you have the LAN world running, you need to find the port that it is running on(Hard To Find Out) , then you need to port forward that particular port on the computer hosting the LAN world AND on the router of the computer, and forward it to the internal IP of the computer hosting the LAN world, then you need to find the external IP of the computer hosting the LAN world, then use that IP and the port to connect.

PS: the port that an LAN server uses changes every time it is started again, the external IP also changes a bit but not as often and at any time. Leaving ports open on you router imposes a security threat on your network, this method is really not worth it, try to create a server using the MC server software