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Homing is a process that occurs in the grbl code that resides on the Arduino. Programs like Easel and most G-code senders will have a command that you can use to tell grbl to home the machine (UGCS uses $H as the homing command).
Once the machine is homed then you can move around among the programs that send G-code and Machine zero is still valid unless you perform a command/function to change it or remove power from the Arduino.
There are lots of things that can cause position errors. Start by reading this: