"Analogy" vs. "comparison": bridging the gap between words

What is similar?
Both "analogy" and "comparison" involve examining two or more things to highlight similarities or differences between them.
What is different?
An "analogy" is more specific and often more complex, typically involving a relationship between two sets of terms or concepts to explain an idea or reasoning. A "comparison" is broader and can be a more straightforward examination of similarities and differences between two or more entities.
Which one is more common?

Examples of usage
Analogy- She used an analogy to explain the heart by comparing it to a pump.
- The teacher made an analogy between the solar system and an atom to help students understand the structure.
- The comparison between the two products highlighted their unique features.
- In comparison to last year, this year's results are much better.