Don't bite my head off... but maybe the fish that has an extra stripe on its butt also has an extra need that should be considered?
I'm useless with Latin names and wouldn't have a clue so I'm a common name gal...but I think it's useful to know exactly what you have so you can be sure how to look after it correctly...in my opinion
In most cases the common name simply is used. The OP is reffering to different species of Corys which names are mixed up in the trade and even of which the common name is derived from the Latin name. C.julii (Corydoras of Juli) isn't in the trade and a look-a-like is sold as such.
Someone mentioned them to be a different species than bought and is completely right.
That doesn't have to do with common ot Latin names but about using the right one. "They are Three Lined Corys instead of Julii Corys" could have been the Common name used.
Also when several species are having the same common name (Leopard Cory, Firemouth, Rubberlip Pleco, Clown Pleco, etc...) it can be useful to use Latin names if you like to be more specific, want to breed them or buy it company of the same species for instance.
If one has altum angels one doesn't want to end up with scalare to join them.
Plain and simple : In normal situations there is not any problem at all to use common names.
We ALL do so.
If they're (easily) mixed up or there is doubt which species we're talking about there can be reasons to use / mention the Latin name.
If people only want to call their fish Cory, Cichlid, Pleco or even plain "fish" they should do that. But this could cause some practical problems in this forum.
There is no right or wrong about this, we're free to do so and there is no law for it as far as I know
But there is nothing wrong to point out the OP has bought himself different fish than thought either.