What is difference between veg and non-veg (as milk is veg but onion is non-veg).?

i m understanding that milk is veg but onion is non-veg. onion produce in earth and mail produce in animal. animal's meat is non-veg but milk is non-veg. what is this i m not understanding. anybody can give me advise.
Update: Milk is produced animal as cow but meat is also produced animal. meat is non-veg but milk is veg that is my confusion both produced by animal one thing is veg and is non-veg. clear it
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