Best refers to their housings as deadbolts and mortise/rim cylinders etc and the part with pins as cores according to their brochures/manuals. I just looked up a few other manufacturers as well. I guess it is just dependent on what/how you learned or your local area as to what a specific person calls them.
Corbin Russwin: Calls theirs LFIC cores: Page 14
http://www.corbinrusswin.com/Other/Corbin%20Russwin/Product%20Pages/Key%20Systems/Pyramid/Downloads/Catalog/45078.pdf
Arrow SFIC: interchangeable core
http://www.arrowlock.com/en/site/arrowlock/Products/?groupId=769384
Medeco LFIC seems to use both: Medeco® Large Format Interchangeable Core cylinders are designed so that cores can quickly and easily be changed... The Medeco® Large Format Interchangeable Core cylinders are available....Cores are available to fit into rim and mortise cylinders
http://www.medeco.com/en/site/medeco/Products/?groupId=915553
Medeco SFIC seem to be cylinders though
http://www.medeco.com/en/site/medeco/Products/?groupId=1154611