"Got" is the past tense of "get". If you got someone something, you acquired (got) something and then gave it to someone else. You needn't necessarily have bought it.

Get and got are similar. Get is the present tense of the verb. For example, "I will get you that". Got is the past tense (it's already happened), for example, "I got you something". Buy is the present tense 买 of the verb. Bought is the past tense of the verb. "I will buy you something". "I bought you something". If you're going to buy something for someone, it's also find to say "I'll get you something".