Slicing and performance

It might be that I don't understand slicing that well. I want to add one list from a particular index to another list. I was wondering, because I read that if you slice a list that you make a (deep)copy of it, which method is faster:

method 1

new_lst += old_lst[i:]

method 2

while i < len(old_lst):
    new_list.append(old_lst[i])
    i += 1

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