Coops are shares owned in a corporation. You have no ownership right over any specific geographical location, just a share in the entire building. That’s why everything must be approved—if you alter something in your unit, you’re altering a piece of the corporation’s holding, not a piece of your property.
Condos are just individual units in a development subject to specific ownership agreements between the condo/development complex and the homeowner.
A tenancy in common is any property owned by two or more people. The property is not divisible, but each owner has a right to their equal share in the property. There are certain specific provisions and rights under law allowed to each owner of a TIC. One of those is the right of survivorship: if one of the tenants dies or sells their piece, the other continues to have the right to own and occupy their piece of the property. This can make it difficult for people who inherit or buy a TIC, as they can do nothing to eliminate the senior owner. The important point is that a TIC represents shared ownership in an indivisible piece of property.