"My mom is writing a book on Thursday."
Translation:W czwartek moja mama pisze książkę.
Well, here's the thing: firstly, if we accept "mom", "mother" is accepted automatically, and the other way round as well, as far as I remember. Similar with "dad" and "father". Even if we actually didn't want that, we can't block them from being accepted.
Now, we've been discussing it a lot, and decided that in most contexts, only "mama" will be accepted for "mom". "matka" will only be accepted if the sentence refers to motherhood in general, like "I'm going to be a mom!" For "mother", "matka" is suggested and "mama" accepted. It's possible that we've missed some sentence and it can be inconsistent there, but that's what we decided upon.
Now, about the 'why': in English, "mother" is more formal than "mom", but still more or less neutral. Nothing special about the word. In Polish, over the years "matka" became even "too formal". It is of course prone to interpretation and personal opinion, but our view is that if you say "moja matka", you are strangely formal and you sound as if you are angry with your mom. This is actually something that a school teacher pointed out to me when I told her something about "moja matka". The same goes with "tata" and "ojciec". It's just too official.