Forget the bread, that's not the determining factor.
Taxonomy is where it'll be decided.
...Sandwiches, are a 'Wastebasket taxon', into which are placed any generally, if not exclusively, diurnal food stuff principally defined by a doughy exoskeleton. While the Weinnerids, hot dogs, wurtzels and false wurtzels are firmly rooted in the wider burger family the Teresimorphia or Minceoformes. Their exact phylogeny however has traditionally been problematically enigmatic. Most contentious has been their occasional inclusion in the Hesperoteresians or true burgers. An alternate proposal has been that they form the polyphyletic sister clade to Hesperoteresia, the Teresidermiads.
All extant true burgers are firmly rooted in the crown group Hesperoteresia whose most basal member is the immediate descendant of, but not including, Steak Tartare (Teres mongoliensis) which arrived in Western Europe from central Asia in the late Holocene.
There certainly were Teresimorphids in Western Europe already at this time, the koftids, rissoles, true pasties, Farcimenopmorphia (true and pseudo sausages), terrines, polpetturyids, including the Scandinavian meatball (Polpettis borealis) and the indigenous British meatball (Faggot faggot) being already well established.
However, like the extinct Mediterranean Isicia omentata, these are all non ancestral forms to the Hesperoteresians and, with the exception of the outlying Farcimenoformes, form a monophyletic group known as the false burgers or Pseudoteresinidae.
While there is firm indication that Weinnerids share strong affinities with Hesperoteresia, their distinct gross morphological similarity to the true Farcimeninae has always been problematic, most especially the sharing a conspicuous dermis, a feature otherwise unknown in any other Teresimorph.
Thus fine phylogentic inference reinforces the view that the Weinneridae represents a monophyletic subdivision within Hesperoteresia is not well supported. And that the otherwise novel features exhibited in Weinnerids and Fascimeninae are not explainable in terms of coincidental phenotypic homoplasy.
Instead it is proposed that the Weinnerids form a distinct polyphyletic group and sister taxa to the true burgers, Stemming from a probable hybridisation event between the proposed most basal Hesperoteresid Teres hiedelbergensis and an as yet unidentified Farcimenoform, where information and material was transported across the dermis....