The term “Core 1.4” refers to the and the game emulation core version . In emulation, a "core" is the heart of the emulator—the code that translates N64 machine language into x86 instructions.
You are a casual player wanting an easy setup, you use macOS/Linux, or you only want to play single-player games (use standard Project64 3.0 instead). Project64k Version 0.13 Core 1.4 Download