La respuesta de Rae es lo mejor. It's rainy today. Igual no llueve ahora mismo, pero lleva la mayoría del día lloviendo, y se espera que lo siga.

"It's rainy today" means it rains for the whole day. "It's raining today" means it rains at the moment you speak. Happy learning.

The difference is subtle. "It's raining today" implies it's raining as you speak, has been raining for some time and/or may continue raining for some time. "It's rainy today" implies that it has been raining today (possibly off and on) or that you expect it to rain soon. It could also mean that it's raining now, as you speak.