An analogy is a comparison between two otherwise unlike objects, people, places, or things that highlights a similarity between them in order to explain or clarify a concept.
The other definitions you provided refer to different literary terms:
- A allusion is a brief or indirect reference to a well-known person, character, or event.
- Connotation refers to the feeling or idea that a word suggests, beyond its literal meaning.
- A theme is a lesson or message that an author expresses through the literary elements of the text.