another (ADDITIONAL)
determiner, pronoun
one more person or thing or an additional amount:
e.g I'm going to have another piece of cake.
"Would you get me a bar of chocolate from the kitchen?" "Another one?!"
We can fit another person in my car.
other (PART OF A SET)
determiner, pronoun
the second of two things or people, or the item or person that is left in a group or set of things:
e.g I've found one earring - do you know where the other one is?
Hold the racquet in one hand and the ball in the other.
Some people prefer a vegetarian diet, while others prefer a meat-based diet.
She gave me one book last week and promised to bring the others on Wednesday.
other determiner
the opposite:
e.g Put the chair at the other end of the desk.
The man was waiting on the other side of the street.