I tend to imagine this confusion came about because Google were just really excited about the fun possibilities of location-aware devices and rushed in without really thinking about what the point would be, but it's entirely possible they just wanted to track your movements and came up with some half-hearted window dressing to con you into willingly consenting being monitored.
One thing I do miss about Latitude is the ability to poll somebody for a location update. It could have been useful when meeting up in town for lunch, though in practice I think I only used it once, trying to find some friends at the Christmas market. Facebook Messenger has the option to stamp each missive with a geolocation, and I'm pretty sure Google Messenger had a location-sharing facility before they retired it in favour of the unified Messenger channel, but "I am here" is just not quite as useful as "Where are you?"
Google are touting Google Plus Locations as the replacement to Latitude but it still doesn't have the "Where are you?" feature - it's the same Location Reporting system Latitude used, with all your subscribing friends' most recent locations plotted on a map. I'm trying it out, even though I recently switched Location History off on my phone because - as nobody else was even using Latitude at that point - I didn't need the drain on my battery. Also, because I had it set up to automatically check in to my work and home*, I think maybe it was flooding my G+ stream with nonsense location posts.
Locations says it needs Location Reporting, which is fair enough. It does not say it needs Location History, but when I went to Locations in G+ on my Android it would not proceed unless I agreed to turn on both. I immediately turned off Location History (in Google Settings), it has not yet complained. That said, it was probably Location Reporting that I think was draining my battery before, not Location History, though it is possible that without Location History it'll be less obsessive about constantly checking in.
(Location Reporting is the part of the Google software that lets any application request your current location be updated from your device at any time. Location History is the part of the Google cloud that stores all your past reported locations. I had it on for about a month, and it happily told me that I was mostly moving back and forth between home and work, except when I wasn't, and I could not fathom for the life of me why I would need to know that. Happily Google allows you to delete your Location History at any time, so I did.)
* I figured it was a good way of climbing the aforementioned leaderboard. It kind of worked, as nobody else was playing.