What properties allow something to be considered "milk"? Traditionally, milk is defined as (from Merriam-Webster):

1: a white liquid produced by a woman to feed her baby or by female animals to feed their young; especially : milk from cows or goats that is used as food by people
2: a white liquid produced by a plant

In today's day and age, if you go to a grocery store (or coffee shop) you can get many varieties of milk: animal milk, lactose-free animal milk, soy milk, coconut milk, rice milk, almond milk, hemp milk, and more.
My question is, is the traditional definition of milk complete? Are there any exceptions to definition #2 of milk (i.e. white liquids produced by plants that are NOT considered milk, or non-white liquids produced by plants that ARE considered milk)? What other properties do all milks share that allow them to be substitute ingredients in the same products?
I will disagree with Johanna here. While hers sounds like a reasonable definition, it is not how the word is used in practice. 

Milk is 


A) Cow's (also goat's, sheep's, camel's and mare's) lactated fluid, or 
B) Any liquid which kinda looks like A), doesn't have an overly strong taste, and there is a convention of being called a milk. It can in many cases be a substitute for A, including when drinking straight out of the mug. 


So not only are there nut milks like almond milk which contain both fat and carbohydrates, but there are also grain milks like rice milk and oats milk, which have practically no fat and get their white color from the starch in the grains. This goes against the "fat in water emulsion" definition, but it is common usage. 

There are also foods which have "milk" in their name while nobody would say that they are a milk, like the "donkey milk" wine. 

In the end, there is no rule. Whatever people call "milk" is a milk. And they call "milk" whatever reminds them of the milk they have encountered before.