What is the difference between intelligence and wisdom in the Buddha's teaching?

Knowledge = bahussutha, intelligence = panna, wisdom = knanam.

In Buddhism, 'wisdom' is something that cuts through & eradicates mental defilements (of greed, hatred & delusion), leading to the ending of suffering. Where as other types of knowledge do not.

To quote:

And what is the faculty of wisdom (paññā)? There is the case where a monk, a disciple of the noble ones, is wise, endowed with wisdom of arising & passing away — noble, penetrating, leading to the right ending of suffering.

SN 48.10

The Kalama Sutta may help here since it lists other kinds of knowledge that are not wisdom:

So in this case, Kalamas, don't go by reports, by legends, by traditions, by scripture, by logical conjecture, by inference, by analogies, by agreement through pondering views, by probability, or by the thought, 'This contemplative is our teacher.' When you know for yourselves that, 'Certain mental qualities are unskillful; these qualities are blameworthy; these qualities are criticized by the wise; these qualities, when adopted & carried out, lead to harm & to suffering' — then you should abandon them.

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The Buddha taught them, and us, not to accept or believe anything immediately just because it fits with any of a number of criteria. He listed ten such criteria for them to be wary of, so they could avoid becoming anyone’s intellectual slave, even of the Buddha Himself. This principle enables us to choose for ourselves the teachings that are truly capable of quenching suffering (dukkha). The ten examples the Buddha gave in the Kalama Sutta follow.

1. Ma anussavena:

Don’t accept and believe something to be true just because it has been passed along and retold for many years. Such credulity is a characteristic of brainless people, of "sawdust brains," such as those in Bangkok who once believed that disasters would befall people born in the "ma" years. (The years of the small snake, big snake, horse, and goat — five through eight in the old twelve-year Thai cycle — all begin with "ma.")

2. Ma paramparaya:

Don’t believe in something merely because it has become a traditional practice. People tend to imitate what others do and then pass the habit along, as in the story of the rabbit that was terrified by a fallen mango (like Chicken Little’s falling sky). When the other animals saw the rabbit running at top speed, they were frightened too and ran after it. Most of them ended up tripping and tumbling off a cliff to their deaths. Any vipassana (insight) practice that merely imitates others, that just follows traditions, will bring similar results.

3. Ma itikiraya:

Don’t accept and believe something simply because of reports and news of it spreading far and wide, whether through one’s village or throughout the whole world. Only fools are susceptible to such rumors, for they refuse to exercise their own powers of intelligence and discrimination.

4. Ma Pitakasampadanena:

Don’t accept and believe something just because it is cited in a pitaka (text). The word "pitaka," although most commonly used for Buddhist scriptures, can mean anything written or inscribed on a suitable writing material. The teachings memorized and passed on orally should not be confused with pitaka. A pitaka is a certain kind of conditioned thing made and controlled by human beings, which can be improved or changed by human hands. Thus, we cannot trust every letter and word we read in them. We need to use our powers of discrimination to see how these words can be applied to the quenching of suffering. There are discrepancies among the pitaka of the various Buddhist schools, so care is called for.

5. Ma takkahetu:

Don’t believe something solely on the grounds of logical reasoning (takka). Logic is merely one branch of knowledge that people use to try to figure out the truth. Takka or Logic is not infallible. If its data or inferences are incorrect, it can go wrong.

6. Ma nayahetu:

Don’t believe or accept something merely because it appears correct on the grounds of Naya or what is now called "philosophy." In Thailand, we translate the Western term philosophy as prajna. Our Indian friends cannot accept this because "naya" is just a point of view or opinion; it isn’t the supreme understanding properly referred to as panya or prajna. Naya or nayaya is merely a method of deductive reasoning based on hypotheses or assumptions. Such reasoning can err when the method or hypothesis is inappropriate.

7. Ma akaraparivitakkena:

Don’t believe or accept something simply because of superficial thinking, that is, because it appeals to what we nowadays call "common sense," which is merely snap judgments based on one’s tendencies of thought. We like to use this approach so much that it becomes habitual. Some careless and boastful philosophers rely on such common sense a great deal and consider themselves clever.

8. Ma ditthinijjhanakkhantiya:

Don’t believe accept something to be true merely because it agrees or fits with one’s preconceived opinions and theories. Personal views can be wrong and our methods of experiment and verification may be inadequate, neither of which lead us to the truth. This approach may seem similar to the scientific method, but can never actually be scientific, as its proofs and experiments are inadequate.

9. Ma bhabbarupataya:

Don’t believe something just because the speaker appears believable, perhaps due to creditability or prestige. Outside appearances and the actual knowledge inside a person can never be identical. We often find that speakers who appear creditable outwardly turn out to say incorrect and foolish things. Nowadays, we must be wary of computers because the programmers who feed them data and manipulate them may put in the wrong information, make programming errors, or use them incorrectly. Don’t worship computers so much, for doing so goes against this principle of the Kalama Sutta.

10. Ma samano no garu ti:

Don’t believe something simply because the monk (more broadly, any speaker) is "my teacher." The Buddha’s purpose regarding this important point is that nobody should be the intellectual slave of anybody else, not even the Buddha Himself. The Buddha emphasized this point often, and there were disciples, such as the Venerable Sariputta, who confirmed it in practice. They didn’t believe the Buddha’s words immediately upon hearing them; they only did so after reasoned reflection and the test of practice. See for yourselves whether there is any other religious teacher in the world who has given this highest freedom to his disciples and listeners! In Buddhism there is no dogmatic system that pressures us to believe without the right to examine and decide for ourselves. This is the greatest uniqueness of Buddhism that keeps its practitioners from being anybody’s intellectual slave. We Thais should never volunteer to follow the West as slavishly as we are doing now. Intellectual and spiritual freedom is best.

Help! The Kalama Sutta, Help!

In Mahayana, intelligence and wisdom are not used interchangeably. Wisdom has various meanings, depending on the context. The issue is that different Tibetan words are translated 'wisdom.' I assume these Tibetan words correspond to different Sanskrit words as well.

In the Abhidharma, it says:

QUESTION: What is wisdom (shes rab)?

RESPONSE: It strongly differentiates the qualities of things that are to be examined. It has the function of overcoming doubt. Just as it has been said above, wisdom is a knower that individually differentiates the faults and good qualities of things that are to be examined.

However, wisdom (yeshe) refers to the cognizer realizing emptiness. There are also three types of wisdoms:

There are three types of wisdom: the wisdom arisen from hearing, the wisdom arisen from thinking, and the wisdom arisen from meditation.

The wisdom arisen from analytical meditation on emptiness is yeshe. It is the one we refer to when we speak of the higher training in wisdom. Or when we speak of cultivating the perfection of wisdom.

Intelligence refers to a mental factor that a student must have. It resembles shes rab. In the Middle Length Lam Rim, Tsongkhapa says:

Someone to whom good ways of explaining appear as faulty ones, due to not having the intelligence to distinguish them, is not a suitable vessel. Therefore one needs to have the intelligence that understands [what is to be abandoned, and what is to be adopted].