OTHER is an ADJECTIVE which refers to a person or thing that is different or distinct from one already mentioned or known about.
OTHER es un adjetivo que refiere a una persona o cosa que es diferente o distinto de algo ya mencionado o conocido.
EJ: Tell me about the other students in your class.
ANOTHER is an ARTICLE which refers to an additional person or thing of the same type as one already mentioned or known about; one more; a further.
ANOTHER es un artículo que hace referencia a una persona adicional o algo del mismo tipo ya mencionado o conocido; uno más; una más.
EJ: I am hungry. Please give me another slice of pizza.