So you are new to this, i will try to explain the differences between all those new terms in a simple manner. First of all you have to know the difference between scripts, AL Plugins, and Mods.
Scripts usually provide new commands for your ships and stations. But they aren't only limited to this, some may change behaviors of existing ships or add new features. Scripts are easy to install, you just have to unzip the package in your installation folder and start your game. Scripts are usually compatible with each other granted they don't do the same thing and granted it's not specified otherwise by the authors. Anarkis Defense System is a script.
AL Plugins are more advanced than regular scripts. They typically provide features like new corporations, factions, invasion of sectors by those factions, and missions. They are usually compatible with each other granted they don't do the same thing. As an example you can't use two “police” plugins or two “sector takeover” plugins in the same installation. Plugins are installed like scripts, however they add a line in the Gameplay/Artificial Life menu allowing you to enable/disable them easily. Pirate Guild is an AL plugin.
A mod is a package that will add new (or change existing) ships, factories, background, music… It may also alter the world (new map, game starts,…). It ranges from a few additional ships to a whole new universe. Mods may or may not include scripts and plugins. To know if 2 mods are compatible is a bit tricky, if 2 mods alter the same files, they aren't compatible. As an example you can't use 2 ship packs at the same time. You can use the X3 Editor to look at the files included in the mods and see if they collide or not. Once you are sure, you can use the False Patch method to use two or more mods together.