Intelligence is the ability to think, reason, and understand without doing things automatically, or by instinct. (Collins English Dictionary)
Intra-personal intelligence (Self Smart) is the ability to be aware of oneself, to understand one’s own feelings, motives and desires, strengths and limitations, and to express one’s thoughts, feelings and desires non-destructively.
Inter-personal Intelligence (People Smart) is the ability to be aware of the behavior of others, and to be sensitive to their feelings, needs and motives, and to establish and maintain cooperative, constructive and mutually satisfying relationships.
There is a distinction between the kind of intelligence which allows someone to solve complex mathematical problems (Logic-Mathematical) or to process large amounts of information (Verbal-Linguistic) and the kind of intelligence which allows someone to understand the emotional complexities of people’s behaviors. These are IntraPersonal and InterPersonal intelligences.