@SMickey,
The examples here are showing "whether" and "if" as part of noun clauses.
There are many more variations such as:
I don't know whether or not she is coming.
I don't know whether she is coming or not.
I don't know if she is coming.
I don't know if she is coming or not.
English is an expressive language, and the difference comes down to formality and emphasis.
The word "if" is much more common and therefore lends itself to the spoken language. The word "whether" is more formal and less used, and therefore is used in more formal spoken and written situations.
To add "or not" adds emphasis to the uncertainty of the speaker.
Of course, "if" is also used in those conditional clauses too. e.g.
"If you don't have an umbrella, you'll get wet". And in a written piece that has a mixture of conditional clauses and noun clauses, a writer may choose to prevent confusion by using "whether" to begin the noun clauses instead of "if".
If you knew if Bill was coming, why didn't you see if Sally wanted to come too?
If you knew whether Bill was coming, why didn't you see whether Sally wanted to come too?
I would personally choose one and stick with it for personal use. If you want to sound more formal, then "whether" will work for you. If you want to sound more casual and laid-back, use "if".
So in a nutshell, sentence 1 is formal and sentence 2 is more casual. The same goes for A and B. Hope that helps.
Jon Petruch
Linguist and English Teacher