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Related to each other. Mashout refers to denaturing the protiens that covert starches to sugars by raising the temperature of the bed to 168-169F. Sparging is rinsing the bed to remove the wort from the mash using hot water to wash the bed. Typically, you would mashout using your sparging water at a temperature just above 168F to offset the lower temp bed.
Different steps, in that Mash Out is optional, and everyone doing all-grain sparges in some fashion. (I don't know anyone that "no-sparges" their grains.)
Mash Out is a temperature raise or infusion that raises mash temp from the saacharification range up to 168F to denature enzymes, as Dave said.
Sparging is the rinsing, and one could batch sparge or fly sparge after mashing, regardless of whether one does the mash out step. In addition to denaturing, the mash out also increases liquidity and improves lautering, and thus efficiency.