The US uses 'mom' and 'mommy'. 'mom' is pronounced like the name 'Tom', and 'mommy' like 'Tommy'.
The only Americans I've heard saying mum and mummy are actually British citizens who immigrated with their mum and dad when they were children. They retained that British usage.I didn't want to chime in too soon, not being an AmE speaker, but I have heard the American 'mom' pronounced like the British 'mum' too. I thought it was nothing more than another spelling difference.
I use three different initial vowels in those words! Mom, was, and trough all have different vowels in my pronunciation. Many Americans (but evidently not me!) use the same vowel for mom and trough./ɒ/, the sound of the (first) vowel of mom, mommy, was, trough, sausage, etc, is close to that of IPA [ɒ].
I use four different initials vowels there./ɑː/, the sound of the vowel in father, far, heart, clerk, half, aunt, etc
You're talking about a British accent (RP, perhaps), right?For those who know their IPA:
/ʌ/, (in the normal BrE phonemic transcription), the sound of the (first) vowel of mum, mummy, come, young, blood, does, etc, in modern standard southern BrE is close to that of IPA [ɐ].
/ɒ/, the sound of the (first) vowel of mom, mommy, was