Thanks for your question to let me look up the definition of the two words:

#insight
The capacity to gain an accurate and deep understanding of someone or something.

Synonyms
intuition, perception, awareness, discernment, understanding, comprehension, apprehension, appreciation, cognizance, penetration, acumen, astuteness, perspicacity, perspicaciousness, sagacity, sageness, discrimination, judgement, shrewdness, sharpness, sharp-wittedness, acuity, acuteness, flair, breadth of view, vision, far-sightedness, prescience, imagination

#Wisdom
The quality of having experience, knowledge, and good judgement; the quality of being wise.

Synonyms
sagacity, sageness, intelligence, understanding, insight, perception, perceptiveness, percipience, penetration, perspicuity, acuity, discernment, sense, good sense, common sense, shrewdness, astuteness, acumen, smartness, judiciousness, judgement, foresight, clear-sightedness, prudence, circumspection

I would say that insight is something that you gain from having SPECIFIC insider knowledge about the topic.  Such as - a cop has better insight about what the criminal was thinking, than I do.  

Whereas wisdom is a more general knowledge that you gain throughout your life.  Pretty much only old people are wise - but someone with insight can be any age.  If a younger person appears wise then we would say "they are wise beyond their years" because wisdom is associated with attaining broad understanding throughout your life.

Hope it helps! :)

It's a good question. 

1. look up the definition of both words

2. look up 10 examples of each word used in a model sentence (preferably in a dictionary)

3. do a google search with each word and see what pops up

4. look up the synonyms and antonyms of each word

5. see which words tend to be collocated commonly alongside each of the words you are looking up

6. ask a native speaker what is the difference

Insight. Like someone already mentioned, the biggest difference between insight and wisdom is duration. Insight is technically related to specific matters. For example, insight into the matter might lead one to understand underlying factors of causation and interrelation.

Look, my insight into language learning leads me to believe that most people learn languages for economic purposes... Also, I am convinced that there is a huge market for would-be language learners who never bother to progress beyond a few basic phrases or lessons. I know this for sure in the abundance of useless language learning products I have encountered. 

Let's say that I want to start a company to teach languages. When I tout the benefits of my company, I should keep in mind that most people are learning a language either to get richer (they need to advance their profession, skills, ability to travel internationally) or either because they're the type of person who is gullible and easy prey for marketing schemes. Wisdom would tell me that I should leave open the message so as not to dissuade any demographic from being my customer base. So, I would not promise anything too outrageous because it might dissuade serious learners who know that language learning requires dedication, motivation, and persistence. But I also wouldn't want to say that unless you're willing to put in dozens of hours a month, you will learn almost nil... that would discourage the casual (fantasy users). 

That's wisdom.