Related: How to Read Literature Like a Professor by Thomas C Foster
symbols in literature are mostly subjective, while allegory is 1-to-1 in meaning
Symbols and allegory are used interchangeably, but they don’t mean the same thing. Both of them refer to something in literature - a scene, a person, an object, etc. - that actually has another meaning referencing something in the real world or concepts in human nature. However, allegory is a 1:1 ratio in terms of literature vs extrapolated meaning, and symbols can stand for multiple things or simply invented by the reader while not intended by the author.
Animal Farm is a perfect example of allegory. It’s very simple and straightforward, and seemed like George Orwell really wanted to get it across to readers. The horse represented people who would just keep working and going along with things until their demise. The Pigs represented revolutionaries who came into power, and turned into the very thing they despised. Symbols, however, can be contested and much more subjective. They can be objects or scenes placed in the story which the author doesn’t intend to have any deeper meaning, however it’s extrapolated by the readers because of their own circumstances, imaginations, or lenses in which they view the piece.
While racking my brains for an appropriate literature reference, the easiest one I can think of is actually Taylor Swift’s songs and how some of her fans have whipped up insane theories based on very small details. Swift has even confessed in interviews that the songs take on new meanings once she puts it out there. I’d say this is related to headcanons in fandom spaces as well.