The term intelligence is used to describe a person's acquiring and applying knowledge and skills. The qualities of someone that is intelligent include curiosity, being open-minded, being enticed easily with deep talks, usually disorganized and alone. On the other hand, intellect is used to describe someone with a good faculty of reasoning and understanding, especially about abstract things.
The qualities of a person with intellect include taking of calculative risks, looking for facts, and thinking based on reasoning. Intellect is objective, as it requires no redundancy, judgment, or exploration. Meanwhile, intelligence is the subject. Intelligence is usually based on the quantity and quality of knowledge that has been earlier acquired, while intellect is considered to be inborn.
Intelligence refers to the ability for your mentality to compute materials, while intellect refers to the mental capacity for materials. It is possible or easier to work on improving your intelligence than improving the intellect.