I think that retailers also often play a part in this! There are many variant models available from the factories for some patterns, In general shops were not obliged to buy 'boxed sets' but individual items and so they were probably retailed in different sets comprising some of the same items, likewise smaller shops will have stocked just a few models and larger stockists may have had a complete selection, from which a 'set' could be assembled.
It's hard to imagine a cologne bottle of this (apparent) size (and weight) without a suitable applicator (or an extended stopper). Usually a bottle that can be shaken into the hand or onto a handkerchief would be somewhat smaller and lighter than this would appear to be.
A careful look for any lip on the decanter might yield a clue about it's designer's intended function. But at the end of the day it's worth remembering that many such items were considered 'multifunctional'.
Given the Belgian connection it could be an absinthe decanter and a bowl for the sugar cubes! ;-)
or a vinegar bottle and a pot for grandma's dentures! ;-) or ....
(whoops, sorry for being silly towards the end!)