"processed food" is generally intended to be less an exact term and more a proxy for "mass-produced food that has been engineered to cost little, last long, and taste good".
Enriching foods with vitamins is generally considered a form of "processing" (i.e. potentially "bad") because we may not fully understand the way our bodies digest the 'original' food with all of its nutrients, compared to whatever nutrients we've managed to discover to put back in whatever is lost in processing. In the case of orange juice, processing may lose vitamins and fiber, and even if we put the vitamins back in, that doesn't guarantee the body would absorb them the same way it would if it ingested the vitamins and fiber together (may not be exactly accurate in this example, but that's my general understanding of the difference)
Enriching foods with vitamins is generally considered a form of "processing" (i.e. potentially "bad") because we may not fully understand the way our bodies digest the 'original' food with all of its nutrients, compared to whatever nutrients we've managed to discover to put back in whatever is lost in processing. In the case of orange juice, processing may lose vitamins and fiber, and even if we put the vitamins back in, that doesn't guarantee the body would absorb them the same way it would if it ingested the vitamins and fiber together (may not be exactly accurate in this example, but that's my general understanding of the difference)