Yes the reversed Kellner or type II Kellner does have a different lens configuration as the Original Kellner or type I Kellner, as I seen it being referred to in some literature, the same literature referred to a Plössl as a type III Kellner! But I suppose we can refer to it as we see fit as long as we are talking about the same diagram, but the most used term is reversed kellner. However I have no interest in the different terms used to refer to the RKE, reversed Kellner, type II Kellner or long spaced König, but only to bring to the attention, of those who are interested, that it is a fine eyepiece when used in F10 to F15 telescopes , which I have, to observe dim doubles, nebula or galaxies and that most of the design, that are still being made, are not called RKE or reversed Kellner!