Realistically, you’ll find that many people will use “whether” and “if” almost interchangeably in casual speech and, in some circumstances, there really is no difference in meaning whether you use one word or the other. That being said, there is a technical difference between the two that arises given certain sentence structures.
In the case of using “whether” in a sentence, though, you may not always see the two very clear and separate choices. Instead, you’ll commonly find many sentence constructions with “whether” that describe one option, but they don’t explicitly describe the alternative. In these cases, there’s a good chance that a “or not” is implied, thus providing the second choice.
I can’t decide whether (or not) to buy these shoes.
Using “if” in a sentence usually indicates a contingency or a condition. Some of you programmers and logicians out there are probably familiar with the if-then construction. This is also how popular online service IFTTT (If This, Then That) came to be.
If I save enough money this summer, then I will buy a new TV.
The exact same idea can be expressed without the “then,” even if you decide to flip the sentence around.
I will buy a new TV if I save enough money this summer.
If we were to swap out “if” in this sentence for “whether or not,” the meaning completely changes:
I will buy a new TV whether or not I save enough money this summer.
When we use “if” in the sentence, the TV will be purchased only if I save enough money. If I don’t save enough money, it’s implied that I’m not going to buy a TV. By putting “whether or not” instead, the sentence then comes to say that it doesn’t matter how much (if any) money that I save. I’m going to buy the TV either way. Instead of “whether or not,” I could also use “regardless of whether” and the meaning would be the same.
Let’s have a look at another pair of examples.
Let me know if you need a ride from the airport.
Here, I’m only expecting a call from you if you do indeed need me to pick you up from the airport. If you arrange for other transportation, and thus no longer require me to come get you, then I’m not expecting you to contact me. Contrast that with this sentence:
Let me know whether you need a ride from the airport.
By switching to “whether” in this sentence, it is now implied that you should contact me whether or not you need me to pick you up. If you want a ride from me, you call. If you don’t need a ride, I still expect you to call. It can be a subtle distinction, but it is nonetheless a distinction.
Some people will say that these little nuances aren’t all that important as long as you get your meaning across, but choosing one word or the other can affect the meaning or connotation. Good grammar still matters, whether you like it or not.