Better, worst or equal time complexity

I was solving an algorithm problem which has to do with combinations from AlgorithmFridays

I defined a function combinate

combinate(combos, string):
    new_combo = []
    for combo in combos:
        for char in string:
            new_combo.append(combo + char)
    return new_combo

I knew the combinate function will run in O(n^2) time complexity (quadratic time).

In other to ensure my solution is accepted in the competition, I knew I had to optimize the combinate function. This is because the function would be called within a for loop which would lead to O(n^3) time complexity.

I later came up with what I think is an optimization. Here is the new combinate function definition:

combinate(combos, string):
    new_combo = []
    repeater = len(string)
    index_c = 0
    index_d = 0

    while index_c < len(combos):
        if index_d == repeater:
            index_d = 0
            index_c += 1
            continue
        new_combos.append(combos[index_c] + string[index_d])
        index_d += 1
    return new_combo

I noticed, that I could use a while loop and extra variables to achieve the same result as using a nested for loop when I found out, that there was a pattern.

Question

Since the while loop relies on index_c to terminate and index_c increases by 1 on every 3 iterations.
Does it have any advantage over the nested loop version in terms of speed???

Better, worst or equal time complexity

Question at the end...

Question