Screenshots of the context menu from viewer version of fullscreen on the left & browser version on the right:


First major problem we see is that even the items that are common to both menus are in different locations on each. Now as to the similarities and differences:
The following appear on both menus (but in different locations on each):
next(file)
previous(file)
first(file)
last(file)
zoom+/-
lock zoom
zoom submenu
auto image size submenu
quick slide show
copy to folder
move to folder
delete
rename
properties
close
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The following items only appear on the viewer version of fullscreen:
crop
select none
selection- swap width/height
set selection size (submenu)
set selection ratio (submenu)
open with (submenu)
set as wallpaper (submenu)
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The following items only appear on the browser version of fullscreen:
open
configure quick slideshow
page (submenu) [multipage files, next, prev, etc]
real size
show mask
edit IPTC data
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In addition, you can't make a selection on the browser version, only on the viewer version.
Now, the reason given for some things not working on the browser version is that you're not in editing mode. This applies to making selections, the menu entries relating to selections, and the crop entry. The open with entry and set as wallpaper entry however, should be added to the browser version.
Additionally, I see no reason at all why the browser version (which is supposed to be the "lite" version) has several entries that the viewer one lacks. The page submenu (for navigating multipage files) & real size entries especially.
If the 2 fullscreen modes can't be merged or made identical o each other, then the browser/lite one should be given a thin border or faint background pattern or some such in order to distinguish it from the other. Having 2 modes that appear the same visually, but do not function exactly the same ("almost" isn't enough) just leads to confusion. Additionally, there should be an option in each menu to switch to the other fullscreen mode. This will server both to relieve some of the confusion, and provide a way for users to quickly access the editing options such as cropping.
Just for comparison purposes, these are the same 2 menus when not in fullscreen mode (again, viewer on the left, browser on the right):


EDIT: For those who are wondering what this is about, see THIS topic and THIS topic.