Magnus means "great", Max(imilian) means "greatest". I think it is not about the meaning but about how common a name is.
Max is common, therefore nobody talks about the meaning.
"You sought a flower and found a fruit. You sought a spring and found a sea. You sought a woman and found a soul. You are disappointed."
"It does not become me to make myself smaller than I am." (
Edith Södergran 1891-1923)