As clarified in errata: each spell can be cast once per long rest.
Volo's Guide to Monsters received an errata in August 2017 that addresses the ambiguity you point out.
Post-errata, the triton's Control Air and Water trait (VGtM, p. 118) now reads:
A child of the sea, you can call on the magic of elemental air and water. You can cast fog cloud with this trait. Starting at 3rd level, you can cast gust of wind with it, and starting at 5th level, you can also cast wall of water with it. Once you cast a spell with this trait, you can’t cast that spell with it again until you finish a long rest. Charisma is your spellcasting ability for these spells.
This makes the answer to this question clear: the limitation is once each per long rest, not simply one spell per long rest. You could cast fog cloud, gust of wind, and wall of water using the trait all in the same day if you wanted.
This correction matches rules designer Jeremy Crawford's earlier clarification in a now-unofficial tweet from November 2016 (as cited in Derek Stucki's answer):
can a 5th level triton cast each spell they have from their racial once per long rest, or can they cast one of them?
A triton can cast each spell in Control Air and Water.
"Once you cast a spell with this trait, you can't do so again until you finish a long rest." It's very confusing wording
This exchange may very well be what prompted the clarification in errata.