The Difference Between 'IF' and 'WHETHER'

Many students of English grammar, native and non-native speakers alike, confuse the adverbial subordinator 'IF' found in conditional sentences: (If I were you, I would study harder) with the indirect speech complementizer 'IF' (She asked if  (WHETHER) you spoke French).  Only the indirect speech 'IF' may alternate with 'WHETHER'.

The difference is not quite clear.  Language experts argue that we use 'WHETHER' when we want to be more formal.  Others believe that we use 'IF' to mark true yes/no questions and we use 'WHETHER' to imply more alternatives.  I noticed that 'WHETHER' is used in situations where the listener is being asked to make a choice.  

For example:

Maria: "Do you prefer Greek or Italian food?"

Maria asked whether I preferred Greek or Italian food OR

Also note that only 'WHETHER' can be followed by 'OR NOT'

I wondered if Maria was coming

I wondered whether or not Maria was coming.