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Dinosauria were originally classified under the class "Reptilia," but what made the significant difference between Dinosaurs and other reptiles were the design of the pelvic girdle, allowing their legs to be straight below their bodies. When dinosaur classification/taxonomy is used, dinosaurs are classified as land dwelling "reptiles." (Though theropod dinosaurs are more closely related to birds.)
The "Dinosaur fish" those kids are referring to are marine reptiles and not Dinosaurs. They don't share the same lineage like crocodilians don't share the same lineage either (this is a common misconception). Dinosaurs come from the line of Archosauria (a group that includes Postosuchus), while Plesiosaurs, icthyosaurs, and pliosaurs do not...although, taxonmically they could be if you said they were. However for that to be effective you'd have to reclassify all genera of marine reptiles and dinosaurs to see what made a dinosaur a dinosaur.
Hope this helps...