A client company is located in its headquarters location, but its Internet computers are colocated in one or more other buildings where they rent out space. For example, a website owner could place its website server on the premises of an Internet Service Provider (ISP), or an ISP could place its network router on the premises of the company offering switching services with other ISPs, or a company could locate in a carrier neutral facility with multiple ISPs available.
Some of these terms are more general and can include data centers that only serve one company in a building owned by that company. The COLO building is definitely a situation where one company owns the buildings and several different companies own the computers that occupy the rented space in the building.