A dishwasher is arguably a fixture where it is plumbed and wired directly to the house and part of the cabinetry. It’s arguably a chattel if it rests on its own weight, has easily detached plumbing and a regular power plug.
To avoid confusion, write it down. If something should be included (or specifically excluded) in the sale of the property, specifically record it in the sale agreement. If in doubt, seek advice!