Why do British, Australians, etc. say mum?

Well think how in any version of English when people say the word mother the vowel sound is pronounced like an elongated 'u' like in much. The m-uuuuuuu-ch. So British, Australians ect. probably say mum from how mother is pronounced at the beginning. American English evolved from British English and so it's spelled mom and pronounced with an elongated 'o' different from the 'o' in the word mother which is pronounced like an elongated 'u'. I know it's not much of a historical reason, but American colonists did speak with British accents at first and that as time passed they were lost and evolved into their own unique accents. I mean also look at all over the U.S. there are different accents and that's because at different times there were larger populations of one sort of people or influences of another and then those accents developed into regional accents. And as generations went on the accents which exist now happened.

"Mama" is spelled "maman" in French.

historical answer? this is a guess, but english is a germanic language and the german word for mother is mutter

MU not MO

Its because they can pronounce the "o" sound, whereas americans pronounce it as a long a (maam or mahm). "Ma'am" is a different word in British English, being used to adress police women etc (equivalent of Sir).

Interestingly South Africans use Mom. And a number of regional British accents (e.g. Welsh, North-east England) use Mam.

Does it matter, as long as you love your mother?

Yeah but the o in mother when pronounced sounds more like a 'u' so abbreviated mum sounds better. You don't pronounce the 'o' in mom the same as you do the 'o' in mother do you? Saying all that, actually across much of the UK people use mam such as in most of wales, the north of england, n.ireland, parts of scotland etc. This is as mom is not meant to be an abbreviation of mother but mommy, mum is mummy and mam is mammy.