Although buildings look the same from the outside the way they are managed is very different. The process for renting in the different types can take from one day to a month from application to approval.
Rental Management This is when a landlord owns the whole building. The rental process from making the application to signing the lease and moving in can take from one day to a week. The building can be a walk up or a large full service building and the management company can manage from 1 to 20 buildings. There is a minimal processing charge for applying for these types of apartments.
Condominium A Condo is a building made up from individual owners and investors who may have more than one apartment in the building. The whole condominium is managed by a hired management company who takes care of the building and processes rentals and sales in the building. From application to moving in can take 2 to 4 weeks. There are extra fees associated with the application and the board package is more detailed in the personal information you have to provide. The main difference between a Condo and Coop is the management does not have the right to turn down a qualified applicant the owner has approved.
Cooperative A coop is a building made up from individual owners, investors are not allowed, who may rent their apartment if the coop board allows them to, and then only for a year or two. The coop board is made up of owners in the building. The board usually requires detailed paper work and an interview with the prospective tenants. The coop board has the right to refuse an applicant even if the owner has approved them. The whole process takes more than a month and even then you might not get the apartment. Similar to the Condominium there are extra fees associated with the application.