Singular: Another=one more, the other=last of the set, plural: other=some more, the other=the rest/remaining of the bunch.( with countable nouns)
Other=some more(eg water), the other=all the rest/remaining(eg water)..uncountable noun.
I don’t want this book. Please give me another( science , literature, history whatever). I don’t want this book. Please give me the other( science).
This food is savory. Others are savory too.(not specific: any food)
I don’t want these foods. Please give me the others(specific: salty ones)
Another = another one.
The other=the other one
The others= other ones.