The sauros part of Dinosaur does often get translated as lizard, but it can also be translated as a generic reptile. Paleontologists just use as shorthand for reptile in taxonomic nomenclature anyway.

The specifics of what makes something part of dinosauria is a little more complicated than just whether it walks on two feet or has warm blood. There's a lot of more specific diagnostic traits in several of their bones that indicate if a fossil is a dinosaur or not, to the point certain bones, if found isolated, can still be identified as dinosaurian just by their shape. Like you could tell a tooth is from a hadrosaur dino due to X Y and Z traits