birth vs hatching

birth and hatching both are nouns.

Word	Noun	Adjective	Verb	Adverb
birth	Yes	No	Yes	No
hatching	Yes	No	No	No

As nouns, hatching is a hyponym of birth; that is, hatching is a word with a more specific, narrower meaning than birth:

birth (noun)	hatching (noun)
the event of being born	shading consisting of multiple crossing lines
a baby born; an offspring	the production of young from an egg
the process of giving birth
the kinship relation of an offspring to the parents
the time when something begins (especially life)

birth (verb)	hatching (verb)
cause to be born