What is the exact difference between a full node wallet and a light node GUI wallet and which of both should I use?
A full node stores the whole Tangle, it needs neighbours to broadcast transactions to and you need a static IP address or any other static address so that your neighbours can broadcast transactions to you.
As a light node you do not store the Tangle and you don't need any neigbours.
You just need to select a host (e.g.
https://node.tangle.works:443) which is a full node itself. This host provides your wallet with all the necessary information to make transaction.
What do I need?
Full nodes need to be online 24/7 and are only meant to run on servers.
If you just want a wallet for your laptop/PC that you turn on when you use it and off when you no longer use it then light node is the right choice for you
I'll quote learn.iota.org here, because they have a good explanation.
The IOTA GUI makes it possible to choose between Full Wallet, and Light Wallet. The Full Wallet automatically runs an IRI (IOTA Reference Implementation) instance in the background, which in turn means that you need neighbors in order to participate in the network and be synchronized. If you run the full wallet, you have no "trust requirements", as you are completely and independently participating in the network.
The Light Wallet makes it possible to connect to a remote node (whether it is your own node, or someone else's), and it's uses to get the latest state of the network, most importantly branch/trunk transactions which are required for making a transaction. When running a Light Wallet, it should be noted that your seed never leaves your wallet, and all the sensitive work (such as signing) is done client-side.
As a normal user you should use the light node.