interval training is a generic term, and HIIT is one possible option to do it. Here is a link to an article right here written by Len Kravitz which provides a lot of information http://www.ideafit.com/fitness-library/hiit-vs-continuous-endurance-trai… .
Internal training need not be as HIGH intensity as the HIIT training. An ‘interval’ could basically consist of literally anything that you are weaving into the client’s normal exercise pattern. For example for a client who ONLY does resistance training, you could add intervals of cardio.