For example, industrial business can only exist in industrial zoned areas, like the industrial park. Multi-family apartment buildings cannot be constructed in the middle of single family housing zoned areas. Zoning is not an iron-clad ordinance, and deviations from the ordinance are allowed if warranted. An example would be a person living in a single family residential area who wants to open up a small business operated in the home. To protect the integrity of the zoned area, notices of the request must be sent to neighboring property owners, and a hearing process must be followed.
Variances deal more with the physical layout of the property, rather than use.
Again, for many reasons, the placement of structures on private property is limited, according to zoning ordinance. An example here would be downtown, where structures are allowed to be built right up to property lines, as opposed to residentially zoned areas, where houses, garages, and other structures are required to be set back certain distances from property and right of way lines. As above, deviations from set-back requirements are allowed. An example would be the owner of a narrow lot who wants to build an attached garage to a house, but finds that in doing so the completed structure would have to extend beyond the set-back requirements. While I have the opportunity, let me answer an often asked recent zoning question.