Marlin "Tune->Bed Z" vs "Tune->Babystep Z" vs Z Offset?
Tune -> Bed Z


http://marlinfw.org/docs/features/lcd_menu.html#tune

Per description in this table, this refers to the Mesh Bed Leveling process. It allows to modify all saved mesh z-offsets by the given amount.


Tune -> Babystep Z


http://marlinfw.org/docs/gcode/M290.html

This just instructs the motor to move the given amount, once, without changing any parameters. 


Control -> Motion -> Z Offset


http://marlinfw.org/docs/gcode/M851.html

Here we are talking about the offset of a z probe (e.g. BL-Touch) from the nozzle.