When Sett's Showstopper moves a unit to a battlefield, does it force an untapped unit to tap/exhaust?

Ruling: Abilities that instruct you to move a unit do not exhaust the unit unless the ability specifically says it does. Showstopper's movement is not a regular/standard move, so the unit does not exhaust.

Nuances:

• Only regular moves (also called standard moves) require exhausting units
• Card abilities that move units are separate from regular moves and follow their own rules