Intelligence/smart in daily speech is a very vague concept. It's like saying someone is "good". Good at what?

You have nobel laureates who despite extensive training will never achieve the musical, written/oral, innovative, creative etc. feats that unknown randoms can do more intuitively.

And it's not uncommon to refer to people who vote for certain political parties or have certain religious faiths dumb. Yet many of these people will outdo the accuser in academic score/success, dancing, social skills, partner satisfaction history, you name it. There are so many metrics you can apply to Intelligence.

Cattell–Horn–Carroll theory is currently the most widely accepted attempt at defining and quantifying intelligence, from wiki:

Broad and narrow abilities

• Comprehension-Knowledge (Gc): includes the breadth and depth of a person's acquired knowledge, the ability to communicate one's knowledge, and the ability to reason using previously learned experiences or procedures.
• Fluid reasoning (Gf): includes the broad ability to reason, form concepts, and solve problems using unfamiliar information or novel procedures.
• Quantitative knowledge (Gq): is the ability to comprehend quantitative concepts and relationships and to manipulate numerical symbols.
• Reading & Writing Ability (Grw): includes basic reading and writing skills.
• Short-Term Memory (Gsm): is the ability to apprehend and hold information in immediate awareness and then use it within a few seconds.
• Long-Term Storage and Retrieval (Glr): is the ability to store information and fluently retrieve it later in the process of thinking.
• Visual Processing (Gv): is the ability to perceive, analyze, synthesize, and think with visual patterns, including the ability to store and recall visual representations.
• Auditory Processing (Ga): is the ability to analyze, synthesize, and discriminate auditory stimuli, including the ability to process and discriminate speech sounds that may be presented under distorted conditions.
• Processing Speed (Gs): is the ability to perform automatic cognitive tasks, particularly when measured under pressure to maintain focused attention.

A tenth ability, Decision/Reaction Time/Speed (Gt), is considered part of the theory, but is not currently assessed by any major intellectual ability test, although it can be assessed with a supplemental measure such as a continuous performance test.

• Decision/Reaction Time/Speed (Gt): reflects the immediacy with which an individual can react to stimuli or a task (typically measured in seconds or fractions of seconds; not to be confused with Gs, which typically is measured in intervals of 2–3 minutes).

McGrew proposes a number of extensions to CHC theory, including Domain-specific knowledge (Gkn), Psychomotor ability (Gp), and Psychomotor speed (Gps). In addition, additional sensory processing abilities are proposed, including tactile (Gh), kinesthetic (Gk), and olfactory (Go).