Rain refers to the water that falls in small drops from clouds.
Rein refers to the band of leather fastened around a horse's head to control it. It's also used in the expressions 'to give free/full rein to something' (=to allow an emotion to be expressed freely), 'to keep a tight rein on something' (=to control something strictly), 'to take over the reins' (=to take control).

Rain se refiere al agua que cae en prequeñas gotas de las nubes.
Rein se refiere a la tira de cuero ajustada alrededor de la cabeza de un caballo para controlarlo. También se usa en las expresiones 'to give free/full rein to something' (=permitir que una emoción se exprese libremente), 'to keep a tight rein on something' (=controlar algo estrictamente), 'to take over the reins' (=tomar el control).