Sorry. Should say, "the rain mad puddles" not "they rain made puddled". Typos.

"Rainy" is an adjective. It describes a time period, usually, like "a rainy day" or "a rainy afternoon." "Rain" is a noun or verb. As a noun, it refers to the actual water drops that fall from the sky, as in "The rain fell on my head." Or " They rain made puddled on the ground." As a verb, "rain" means the action of the water falling. "It is raining today."

rain -- noun rainy -- adjective wind -- noun windy -- adjective