To be honest, you can use those words interchangeably most, if not all of the time. Reserving and booking effectively do the same thing: they are both the act of requesting that a certain thing be set aside or guaranteed for your use at a certain time. The only two uses of "to book" that I can think of that really don't fit "to reserve" would be the following: 1) Oftentimes, we use the verb "to book" when referring to someone who is being put in jail. When a criminal is "booked" into the jail, his or her paperwork is processed, and the prisoner is processed appropriately. 2) A common English idiom uses "book it" as a verb that would be similar to "hurry." Here's an example: "When he saw his crazy ex-girlfriend, he booked it out of the building!"

Although generally interchangeable, I would say the difference is that reserve is more likely to be used for something that is limited or relatively limited by quantity, quality, etc. For example, hotels generally have rooms available so one would "book a hotel." For a international flight that fills up quickly "to reserve" makes a bit more sense. However, for a high frequency flight like SFO to LAX or Seoul to Jeju, to book a flight would make sense since there isn't as much problems with a "limited supply." I hope this answers your question :D Also, book and reserve can mean other things but since you were comparing the two I assume you were comparing the similar definitions of "to schedule" something/