That's a language-dependent ambiguity; this sort of "noun¹ noun²" construction in English is actually rather vague, and it can be used multiple ways:

• material - e.g. fish fillet (the fillet is made of fish)
• purpose - e.g. fish knife (the knife is made to handle fish)
• destination - e.g. fish food (the food goes to the fish)
• inalienable possession - e.g. fish tail (the tail belongs to the fish, and removing it means removing part of the fish)
• alienable possession - e.g. fish bowl (the bowl "belongs" to the fish, but you could give it another bowl)
• etc.

As such I believe that in at least some languages it's probably clear if you refer to chicken egg as "an egg coming from a chicken" or "an egg a chicken is born from". Not that they're going to use it with this expression though.

For reference. @cuerdo@lemmy.world used as an example "my penis":

If I say “my penis”, it is likelier that I am talking about the one attached to me rather than the one I bought in the market.

In Nahuatl both would be distinguished: you'd call your genitals "notepollo" (inalienable possession), and the one you bought "notepol" (alienable possession). (Note: "no-" for the first person. For someone else's dick use "mo-" when speaking with the person, i- when talking about them.)

Just language things, I guess.