First, the meaning is different.
1. Mom means: Mom.
2. Mom means: Mom; Meeting minutes; the middle of a month
3. Mother means: mother; mother
Second, the usage is different.
1.mom Usage: followed by a verb or adverb, as a predicate in a sentence.
Example:
My mother used to make the best peanut candy.
My mother used to make the best peanut candy.
2. usage 2.mum: used as a prepositional attribute and an object complement in a sentence.
Example:
If your mother finds out what you have done, you will be in real trouble!
If your mother finds out what you have done, you will be in trouble!
3. Mother usage: when used as a title, it refers to someone's proper noun without an article in front.
Example:
It happened that my mother was not at home that day.
My mother happened not to be at home that day.
Third, the emphasis is different.
1.mom emphasizes: used in the simple past tense.
Mumfocus: used in the simple present tense.
3. Mother focus: used in the simple present tense or the simple future tense.