There are three broad categories of home ownership: freehold, condominium and cooperative.
Freehold homes offer the most privacy and freedom of choice of any other type of home. As owner of the entire structure and grounds, homeowners are free to decorate and renovate as they please. But with that freedom comes a lot of responsibility. All of the maintenance (indoors and out) is the sole responsibility of the owner, which can be costly in terms of both money and time. Freehold ownership is the most common type of home ownership.
Condominiums are typically a less costly alternative to owning a detached house. With a condominium, you own, and are responsible for, the interior area of your unit (everything from the plaster in). Upkeep of the building and grounds is handled by the condominium association, which is funded by monthly fees collected from tenants. Condominiums often have strict rules regarding noise, use of common areas, renovations etc. Condo residents often enjoy less privacy than residents of detached homes.
Cooperatives (or co-ops) are comparable to condominiums, except instead of owning your unit, you own a percentage of shares in the entire building (or complex). As with condominium ownership, maintenance and repairs are paid for through the collection of monthly fees and you are subject to the rules and regulations of the co-op board. One drawback to living in a cooperative is that if you decide to sell your shares and move out, the co-op board has the right to reject your prospective buyer.