I've heard both of these terms used frequently. What is the difference between a Data center vs. a Data warehouse? Are these terms interchangeable?
Also a Data Warehouse may host many Data Marts
So there can be one or more Data Marts, that exist in a Data Warehouse that is hosted in a Data Center that may contain more than one Data Warehouse plus other services.
A data center is a physical facility where (usually) multiple companies' computers are located. It is often so that servers can have a larger-bandwidth Internet connection than the company can get in their own facility, as well as having people dedicated to facilities management, including cooling, power, fire prevention, security, etc.
A data warehouse is a type of database, or a manner of using a database, to collect large amounts of data.
They are not even remotely interchangeable terms.