Zoning is pre-dispute planning where the government restricts the purposes that land can be used for in order to prevent nuisances.
A zoning ordinance can only be found unconstitutional if its "provisions are clearly arbitrary and unreasonable, having no substantial relation to the public health, safety, morals, or general welfare." Village of Euclid.
A special use permit, also called a conditional use permit, allows a parcel to be used in a manner it is not zoned for, but the ordinance must also authorize officials to grant permission for this specific use.
Most zoning acts allow boards to grant variance from the strict letter of the zoning ordinance. This allows an alternative when individual landowners would otherwise suffer special hardship from the application of the ordinance, but it should be exercised sparingly.