"As" can be used in two ways to show that things are equal: "the same **** as" and "as **** as" (e.g., "He is the same age as his friend"; "He is as old as his friend").
"Like" is not really used for comparison in the linguistic sense (that is, it is not a "comparative") but rather to show similarity. So you could say, "She is like her sister" or "She and her sister are alike in many ways," but you're not comparing specific things. You CANNOT say, "She is the same like her sister"--you must say either, "She is like her sister" or "She is the same as her sister."