sprinkling vs rain shower

sprinkling and rain shower both are nouns.

Word	Noun	Adjective	Verb	Adverb
sprinkling	Yes	No	No	No
rain shower	Yes	No	No	No

As nouns, rain shower is a hypernym of sprinkling; that is, rain shower is a word with a broader meaning than sprinkling:

sprinkling: a light shower that falls in some locations and not others nearby
rain shower: a brief period of precipitation

Other hypernyms of sprinkling include shower.

sprinkling (noun)	rain shower (noun)
the act of sprinkling water in baptism (rare)	a brief period of precipitation
the act of sprinkling or splashing water
a light shower that falls in some locations and not others nearby
a small number (of something) dispersed haphazardly