Interesting question. I'll make a 'stab' at an answer.
A 'vacation' is time away from the ordinary routine/ordinary responsibilities. Yes, one typically thinks about time off from work, but retirees also take vacation. HOW one spends (or invests) his/her time during that vacation can vary.
A vacation can be taken in one's own hometown....ala the 'stay-cation,' if they are going to see/do things they may not normally do. One can use his/her vacation to chill on a beach or to do something to help humanity (medical outreach in impoverished areas), or they can travel for pleasure.
The 'travel for pleasure' can be approached two different ways: 1) a leisurely escape (think renting a Tuscan villa), waking up when wants, visiting various villages on no set timetable, etc. OR 2) they can be on tour, which I think of as having a somewhat predetermined schedule. Tours vary in group (more structured with more rigid scheduled) or individual (where one merely hires local guides to share information on a schedule the individual sets.....or they may self-tour, with some idea of what they want to see/when.
To me that is the difference between a vacation and a tour........the structure. All the various approaches have different advantages. Usually when we are on a group tour, we come home rather exhausted, but fulfilled, as we have seen a lot very efficiently.......advantages are just that: the efficiency, not having to 'work' to make arrangements, and the ability to enjoy one's fellow travelers (usually somewhat like-minded individuals). On an individual tour (where one hires his/her own guide(s), that can be arranged where one also has a driver (the least stressful approach for us), but it is usually a bit more relaxing, as you can leave a site sooner, if you are finished enjoying it, or you can stay longer, without feeling rushed. One can also choose to sleep a bit later the next morning after a full day of touring or long road trips....no bus to catch, etc. Depending on where one is touring, the individual approach can be much less expensive, or it can be much more expensive.
Packaged tours have appeal when one just does not have the time to do all the research, or they want the convenience/comfort of knowing every single detail will be taken care of (hotels will be nice, won't have to worry about getting from point A to point B...won't have to worry about parking, tolls, getting entry tickets or standing in long lines...and often, one does not have to worry (as much) about not being fluent in the local language.
We've traveled with a variety of approaches, and most likely we will continue to select different varieties based on where we are going and what we want to see/do. Sometimes cruises make sense, too, when it is just nice to wake up in a new location without losing daylight hours to travel.......just depends on the itinerary. We select the method/provider based on what seems to make sense and what is the the most appealing for each locale.