I always assumed that it was a loanword though, and that 娘, 母親 were the "original" words for mother.

Curiously, "ma" is always the first syllable that is taught to students of Mandarin (to explain the tones).

Apparently it is not a Western loanword - http://wold.livingsources.org/word/77161647552647739

Strictly speaking, "ma1ma" is equivalent to "mummy/mommy" and "mu3" is the formal "mother".

The same in Lithuanian. The more formal version is "motina".