Yeah, Sense of Interval is "naming" the interval (minor, major, #9) versus Interval Sense "feeling" the interval. When improvising, you don't tell yourself "now I'm going to go flat five and then chromatic it to the dominant 7th then resolve on the root". You just feel it. I think he's trying to say develop an mind to ear to muscle memory for the intervals versus being conscious of what those intervals are. This is such a special ability, that you can just sit in on a song with little knowledge of it and be able to improvise on mind-ear-muscle memory and capture the mood based on the intervals you are feeling.