Salts are formed (formally) from acids and bases in the neutralization reaction
2NaOH + H2CO3 = Na2CO3 + H2O
So that's a yes then presumably: Sodium Carbonate (Na2CO3) IS a salt.
In the equation you've given there is a base (Sodium Hydroxide NaOH) and an acid (Carbonic Acid H2CO3) making a salt and water. I think our teacher might have said it wasn't a salt so I was confused by that.
I was also confused by the information that an acid and a carbonate makes salt, water & carbon dioxide, as the implication seemed to be that the carbonate was not a salt.
So what about Calcium Carbonate, CaCO3, presumably that too is a salt? Let me think this through:
A base + an acid --> salt + water
Calcium Hydroxide + Carbonic Acid --> Calcium Carbonate + water
Ca(OH)2 + H2CO3 --> CaCO3 + 2H2O
Am I right?
(PS what age is "High School"? I'm in the UK and am doing GCSE chemistry, usually done at 15-16ish years old, although I'm rather older than that!)