data structures – some misunderstanding in concept of Huffman algorithm

What is difference between Average length of codes and Average length of codewords in Huffman Algorithm? is both the same meaning? I get stuck in some facts:

I see a fact that marked as False:

for a text that it’s characters get from set of n alphabets then
average length of codes is O(log n).

I ran into a bigger challenge when see these two facts:

The average codeword length in Huffman’s algorithm is Omega(log n).

The average codeword length in Huffman’s algorithm is O(log n).

I need a very small example to clear the difference between these concepts.