Intelligence is the ability to acquire information to create knowledge and skills. Information is what is conveyed or represented by a particular arrangement or sequence of things.
From these definitions I can recognize two basic types of intelligence. Intellectual intelligence and emotional intelligence.
Emotional intelligence is the most basic intelligence, but it is taken for granted. Intellectual intelligence is the type that is conditioned by our education systems and is a prized possession for many people. Intellectual intelligence encompasses all learning and becomes biased towards specifics like music, mathematics, science, and medicine to name some.
I can not say which is less common because both types are always involved in any creative way of living and all life is creative by degrees.