What is the difference in meaning and usage between 母 (haha) and お母さん (okāsan)?
母 and お母さん differs in the level of politeness the speaker uses to address someone and changes based on the situation. As rule of thumb 母 is humble and お母さん is respectful. So if your addressing your mother you would call her お母さん on the other hand when talking about your mother with someone else calling her お母さん would come off as rude, so you call her 母, but would call the other person's mother お母さん.
In general Japanese makes a great deal of linguistic distinctions based on the relative social positions of the speaker and listener. You can check out more here https://en.wikipedia.org/wiki/Honorific_speech_in_Japanese.
Easy way to describe the difference is,
母 (haha) = mother お母さん (okāsan) = mom
When a grown-up talks about his or her mom with someone else, it's funny to say "My mom is xxx." Well, it may not be so uncommon in English-speaking world, but in Japan, unless you are in elementary school or younger, you are expected to describe your mom as "mother." It's simply more formal.
Like H. Ha said, it's also possible that お母さん can be used by the person who describes herself. Though the sentence in the example,
does not sound natural Japanese unless there are sentences before or after this one.
Anyway, there are several more ways to commonly describe "mother," but these two are probably the most common ones.
When you describe your mom, you'd want to use 母, while when you describe someone else's mother, you hardly say 母. You need to say,
"あなたのお母さん" or "あなたのお母様" = "your mom"
Hope this helps.
お母さん (okāsan) is more colloquial, and can be used as YOU (second person).
These answers seem good: https://hinative.com/ja/questions/1826
ex. お母さんは愛しているよ。 (mom says) I love you.
Great point. お母さん can be 1st person.
or it can mean "your mother".
Thanks for the note re: *[お母さんは愛しているよ。] not being natural Jp.
If Fujiko Hemming were a mother (or if Kuwata Keisuke was female and a mother) (or if 忌野 清志郎 were alive, and ...), she would say that.
追記 ： たしかに *[お母さんは愛しているよ。] ってのは少し不自然なんだが、 きょうび日本全国で毎日 数百人（またはそれ以上）のお母さんが自分の子供に *[お母さんは愛しているよ。] と語りかけている、と想像するのは、それほど困難ではないでしょ。