When I read about story points it is always mentioned that they should be used because they are a relative measure with examples like:
It takes me 60 minutes to run a trail while you only take 30 minutes to run it. So time is not a good measure to communicate the effort. Miles would be a better choice because a third party could then estimate their individual time based on their own speed.
However you could just as well do the same with time estimates. I say it takes me 60 minutes and you know that you are twice as fast so you can conclude that it will take you 30.
Story points: time = storypoints / individual velocity
Time estimation: time = basetime / individual velocity
So what is the difference and why should I use story points.
EDIT:
It is also mentioned that story points are relative since they are assigned in respect to a reference story. However you can do just the same with time. I.e. Reference story A is assigned 1 base hour instead of 1 story point.
So the advantage of story points as I see it is simply this concept: Don't give a ballpark figure, but rather estimate in relation to a reference point. But as soon as you assign a measure to the reference it does not matter if it is points or time. The result is the same.