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?
A data center or datacenter (or datacentre), also called a server farm,1 is a facility used to house computer systems and associated components, such as telecommunications and storage systems.
Data warehouse is a repository of an organization's electronically stored data. Data warehouses are designed to facilitate reporting and analysis
Also a Data Warehouse may host many Data Marts
A data mart is a subset of an organizational data store, usually oriented to a specific purpose or major data subject, that may be distributed to support business needs.
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.