The similarities between frogs and fish can help illustrate certain concepts in biology. For example, explaining why they are both vertebrates can help someone understand what defines a vertebrate. Frogs and fish have several such similarities.
Both frogs and fish belong to the phylum Chordata and the subphylum Vertebrata. This means that both frogs and fish have a spinal cord and backbone. In addition, all chordates have bilateral symmetry. This means that they have a matching left and right side. Frogs and fish share these traits with other vertebrates, like mammals and reptiles.
Both frogs and fish are exothermic, or cold-blooded. This means that they cannot control their body temperature by internal means. Animals that can control their body temperature are called endothermic or warm-blooded. Fish do have some exceptions to this. Both the tuna and the salmon shark have the ability to increase their body temperature by a few degrees relative to the environment.
Water and Land
In general, amphibians like frogs live on both land and water, and fish live in water. However, some fish can live on land, and some frogs can only live in water. The climbing perch (Anabas testudineus) is a fish that can breath air and crawl along land for short distances. The African dwarf frog (Hymenochirus spp.) usually spends its entire life living underwater. So both groups have overlapping habitats.
Both frogs and fish usually lay eggs in water. However, both have exceptions to this rule as well. Some fish, like guppies and certain sharks give live birth instead of laying eggs. And certain toads, close relatives of frogs, give live birth as well. So most frogs and fish lay eggs in water, but a few give live birth instead.