How can rules 563.2.c.3 and 563.2.c.4 both apply when one says a target that moves zones and returns is still legal, while the other says if something moves to/from a Non-Board Zone it's no longer the same object?

Ruling: Rule 563.2.c.4 only applies when a target changes zones to or from a Non-Board Zone. As long as the target stays on the board the entire time (moving between board zones like battlefield and base), it remains the same object and rule 563.2.c.3 applies.

Nuances:

• The key distinction is "Non-Board Zone" - moving between board zones (like battlefield to base) does not trigger the "not the same object" treatment
• Only movement involving non-board zones causes the target to be treated as a different object