After reading and watching the course videos, here are my inferences

What are the differences between testing intelligence and knowledge?

Testing for intelligence is testing one's ability to think and process knowledge into a solution while testing for knowledge involves testing one's ability to remember what they have been taught.

Intelligence is greatly affected by one’s natural brain cell formations that lead to their ability to solve problems (Nature-based development of the brain) while knowledge is more artificial, acquired through education both formal and informal.

I have a belief that intelligence contributes to one's ability to acquire knowledge and this could be a correlation between intelligence and knowledge. This could mean that someone who did well in an intelligence test is more likely to perform well in a knowledge test.

When might each approach be appropriate or inappropriate?

Intelligence testing is very difficult since there are so many factors that need to be considered while deriving and administering the test. I have grown up and lived all my life in Africa and if an IQ derived by a person who has grown up and lived his all life in Europe is given to me, I am most likely to score between Idiot and moron because it's very difficult for him to test me same as me testing the person from Europe. It's even difficult in Africa, people from crop-growing communities might not be able to test well the intelligence of people from pastoral communities or hunter communities.

Testing knowledge becomes easier because all you have to do is expose people to a knowledge base and test them based on what was contained in that knowledge base.

I believe the best test of intelligence is long term not instant IQ questions or aptitude tests. The best measure of intelligence has to be done for a certain period. Observing one's ability to make use of the knowledge and applying it in life checking how they solve problems using the knowledge they have been exposed to.