The differences are: zero article; indefinite article; definite article; plurals If you haven't learned those you won't understand the differences.

Other - something different from what you are currently doing/looking at. Eg. I don't like this shirt. I want to look at other ones. Another - something different from what you are currently doing/looking at, but exactly ONE other thing. Eg. I am bored with this activity. I want to do another one. The other - a different SPECIFIC option from what you are currently doing/looking at. Eg. You give me a choice of a blue cupcake or a yellow one. I say, "I don't want the yellow one. I want the other one." Others - all the rest of the options. Eg. I only eat the red M&Ms. I never eat the others.