Difference between Sphyraena obtusata and Sphyraena novaehollandiae
I think you may have looked at these species too quickly. 

They are in fact different species. 

Sphyraena obtusata is referred to as the obtuse barracuda, the striped barracuda, or various other names that your linked website (fishesofausralia.net) provides:


  Dingo Fish, Obtuse Barracuda, Pike, Sennit, Short-finned Seapike, Short-finned Sea-pike, Short-jawed Sea-pike, Striped Sea Pike, Yellowstripe Barracuda, Yellowtail, Yellowtail Barracuda, Yellowtail Sennit


Sphyraena novaehollandiae, on the other hand, is referred to as the Australian barracuda, arrow barracuda, Australian sea pike, sea pike, snook, or shortfin barracuda. 


Even your linked post doesn't provide "striped barracuda" as a common name for this species. 


Differentiating the two species:

Your fishesofausralia.net links demonstrate these fish are found on different sides of Australia (S novaehollandiae in the south and S. obtusata in the North of Australia. 

The Wikipedia articles for these fish (linked previously ion my answer) indicate that S. obtusata only reaches maximum lengths of 55cm, while S novaehollandiae can reach sizes exceeding 1 meter. 

Both sources also list a number of additional color and morphological variations you can use to differentiate the two species.