OFFSET is the unavoidable difference between the inputs of any differential amplifier, when both inputs are supplied by the same voltage, i.e. inputs short-circuited. In case of a single input amplifier this means short-circuit between the single input and its (fixed) reference voltage level, often GND.
Full-Scale register is a register, where the calibration cycle - initiated after each change of a channel's gain - automatically stores the input's full-scale value for this gain. It is initialized for each chip and for each channel for gain=1 by the factory. Can be read and overwritten by the user.
Both offset and full-scale value can be calibrated and stored automatically.