A person's take on something is that person's opinion about that thing, usually on a subject that is clearly a matter of opinion.
My take on Woody Allen is that his humor depends on self-put-downs .
A person's understanding of something (in a simian construction) is a statement of fact, or at least of alleged fact.
My understanding is that Omicron is more infectious than Delta.
The word "understanding" can also be used in quote a few other ways, of course.
- I thought that you and I had an understanding.
- At that time his understanding of English was quite limited.
However "take" is significantly more in formal and casual than "opinion". It is also a bit vaguer, and someone's take on something could include both an opinion and supporting beliefs about the facts on that issue, particularly when the facts are not known with certainty.