Welcome to the Forum! Emulation Station is a Front End GUI/launcher than can theoretically be used with ANY emulator (as can AdvanceMENU). The SD Card Images RetroPie and UltraSlim make use of it but are, for the most part, RetroArch (cross-platform portable, modular, multisystem emulator) underneath. With regards to the Game Genie, some emulators can directly use the original Codes (Fceux: Famicom/NES is one of them) although many have their own versions of 'Cheat Codes' that can be exploited if you so wish.
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