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Alguien vs. algo

The Spanish words alguien and algo are both indefinite pronouns used to refer to something unspecified. The fundamental difference between them is that alguien always refers to a person, while algo always refers to a thing, idea, or action.

Alguien

A1
This word translates to someone, somebody, anyone, or anybody. It is exclusively used to refer to an unknown or unspecified person. Think of it as some person.
Alguien está llamando a la puerta.
(Someone is knocking on the door.)
¿Hay alguien aquí que hable inglés?
(Is there anyone here who speaks English?)
Vi a alguien que se parecía a tu hermano.
(I saw somebody who looked like your brother.)
Necesito que alguien me ayude con estas cajas.
(I need someone to help me with these boxes.)
Si alguien encuentra mi cartera, por favor avíseme.
(If anyone finds my wallet, please let me know.)
Creo que estoy enamorado de alguien.
(I think I'm in love with someone.)

Algo

A1
This word translates to something or anything. It is used to refer to an unspecified object, thing, idea, event, or action. Think of it as some thing.
Tengo algo importante que decirte.
(I have something important to tell you.)
¿Quieres comer algo antes de irnos?
(Do you want to eat something before we go?)
Algo huele muy bien en la cocina.
(Something smells very good in the kitchen.)
Busco algo interesante para leer este fin de semana.
(I'm looking for something interesting to read this weekend.)
Pasó algo inesperado en la reunión.
(Something unexpected happened at the meeting.)
Siento que me falta algo en la vida.
(I feel like I'm missing something in life.)

Summary

In short, the distinction is clear and simple. Use alguien when you mean someone or somebody (a person). Use algo when you mean something or anything (a thing, idea, or action).