hmmm... looks like my tank...
Well they are all characins so your reference is valid. Many consider the hatchets to be 'tetras' as well since the term references the trait they all share, 4 ('tetra') unpaired fins--dorsal, caudal, anal and adipose--which all Carnegiella (hatchets) possess.I haven't seen all 4 lately... but my experience is to lose 25% of the tetras typically... so that wouldn't be unusual ( I know the hatchets aren't really a tetra ) but all the sellers list the hatchets and pencil fish together, with the tetras... so they must be similar, or at least by association