When and where are Pluto and Neptune closest to each other? I found two sources sort of answering this question, but conclusions I made of them contradict each other. 
https://www.reddit.com/r/askscience/comments/29jrvq/what_is_the_smallest_possible_distance_from_pluto/ - here is stated that Pluto and Neptune never come closer than two billions kilometres from each other.

Yet from picture in here (I am aware it might be not to scale) Can Pluto and Neptune collide anytime in future? it seems that Pluto and Neptune got a lot closer to each other shortly after 1999 than a half of Neptune orbit radius, judging by their speeds and positions in 1999.

So, how is it? How close can they get to each other and when is it going to happen next time?

Tried to use wikipedia, but while article about Pluto contains information at least about when it was in Aphelion, article about Neptune does not any such information (or I could not find it).
Per page 13 http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1965AJ.....70...10C&amp;defaultprint=YES&amp;filetype=.pdf (it's Harvard, so relatively reliable):


  the closest approach of Pluto to Neptune is locked in near aphelion
  and the minimum distance between the bodies is approximately 18 a.u.


which works out to roughly 1.7 billion miles or 2.7 billion kilometers.

The image from the other answer:



is deceptive if not outright incorrect (tineye shows 15 results, some of which seem reliable, but I couldn't find the originating source).

Notice how much Pluto moves from 1979 to 1989, compared to how much Neptune moves in the same period. It seems that Pluto moved a lot more, but, since Pluto was about the same distance away as Neptune, it should be moving at nearly the same speed, not faster.

As Stellarium shows, Neptune and Pluto are about 40 degrees apart in 1999 (as viewed from the Sun) significantly more than the diagram in the other question indicates (this might be an artifact of the planes being tilted 17 degrees and an unusual perspective view):



(Pluto is invisible but at the center of the cross-- the bright object nearby is 13 Oph, not Pluto).

A perhaps more interesting question: what is the closest approach of the two orbits, even if the planets in question aren't occupying that given point in the orbit.