Mom, Mum, Mam: Different words?

Today, i'm protested when one of my friends call me mam, i said that i'm not a mam yet ^_^. But, he said that mam is a summon for a young woman as a honor. Then, because I'm the lady of KEPO, harus tau dong gimana sebenarnya, that's why i tried to find the reason, here it is: 

Source: http://dialectblog.com/2011/04/07/mom-mum-mam/

I’m reading Louisa May Alcott’s Little Women right now. Throughout the book, the March sisters refer to their mother as “marmee.” This looks like an odd term of endearment until you remember that Alcott grew up (and set her book in) Eastern Massachusetts. Given that her accent was probably non-rhotic (i.e. she dropped her r’s), “marmee” is essentially a different way of writing modern-day mommy.

This got me thinking. We have several informal words for “mother” in English: mum (heard in much of England), mom (heard in much of America), and mam (heard in Ireland and Northern England). But are these actually different words, or are they just, in some sense, the same word?

Although “mum,” “mam,” and “mom” read differently, they’re often pronounced in a very similar way. Here’s a comparison of three different dialects, and their “mom” pronunciations (don’t worry if you aren’t proficient in IPA — I’ll explain after):

London: “mum” — [mɐm]
General American: “mom” — [mɑm]
Manchester, UK: “mam” — [mam]

Whether you understand the IPA symbols above or not, the point is that in these three dialects, the words are quite close in pronunciation. To be fair, there are some regions where this is not the case. In the Western US, for example, mom is often more clearly “mawm.” Still, is it possible that mom and mum and mam began as different spellings rather than different words?

I suspect this may be the case because written usage of them seems fairly recent. Mom andmum appear to only date back to the 19th Century in written form. I’m curious if perhapsmam is the earliest of these, and mom and mum were just different ways of rendering this.

But that’s all I can say for now. I’ve been able to find little information as to whether these words have some common derivation. Google searches of “mom vs. mum” or “mom mum mam” don’t yield anything substantial. I haven’t found much info about their etymologies either. Any thoughts?