Hi. The primary difference is that with a 'stand alone' house like a ranch, colonial, victorian etc you own the house, the land and everything in between (including the airspace - down to the plumbing). With a townhouse/condo (both referred to as 'condominums' in legal terms you own the 4 walls and everything in between. With the rest of the property you are in a sort of a 'co-op' situation where you share ownership with the other condo owners. There are also other issues/concerns to take note of when buying a condo vs house such as HOA (home owner association) fees and condo rules. There are more details involved but those are the primary differences in my professional opinion.
And condominium complexes do differ in pet policies. Society Hill in Newark does allow pets while the Pointe in Union (if I'm not mistaken) does not.