Im gonna explain all of the above mentioned terms in the case of video games, Modded means in the original format of a video game adding alterations (done by players) and changing one or more aspects of that said game. Cracked means if a video game/software requires either a passcode or wont simply work on that console, programmers would alter the game/software and make it accessible for users without those limitations. Hacking means typically infiltrating that software and getting all the codes to either alter or steal it. Patched is somewhat the same to Modding to some extent but it usually involves adding new material to that software for example if you know PES (the football video game) it hasn't registered most teams kits and names so with out altering the code on the game you create a new code to be added to the original game which involves kits and names etc, or its just another way to fix bugs and other security vulnerabilities well after the softwares release.