How does continuous integration relate to continuous delivery / deployment?
Continuous delivery and continuous deployment both take continuous integration one step further, by adding a 'deployment to production' step to the process.
The difference between continuous delivery and deployment is that for delivery this step is done manually and for deployment is it automatic. 



Difference between Continuous Integration, Continuous Delivery and Continuous Deployment. Picture copied from codeproject.com

Whether you do continuous delivery or continuous deployment is very much an implementation choice. If you do continuous deployment, changes in code will be deployed automatically after the acceptance tests are passed. This may or may not be desirable for your product. With continuous delivery, people can make a choice whether a particular code change  is deployed or not (and possibly where exactly it is deployed). 

Since the difference between continuous delivery and deployment is small and many people are unaware of the exact difference, the two terms are sometimes used interchangeably.