There are quite a few difference between amphibians and mammals. However the most unique thing about them is their respiratory system.
Often amphibians will have a larval form which breaths using gills, then undergo a metamorphism into an adult which breathes using lungs. Such as a tadpole to a frog.
The Olm for example, is a salamander which retains both gills and lungs in its adult form. However its lungs contribute very little to the actual respiration process.
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Another example is the tiger salamander. The image on the top left is it at its larval form. Notice the gills sticking out of its neck. At this stage it lives exclusively in the water.
The image to the bottom left is the adult form. During specific environmental pressures the tiger salamander will undergo a metamorphosis. Trading its gills for lungs, and living on the surface.
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However there are some amphibians which break this rule.
Another example is the Plethodon montanus. Like most amphibians it breathes through its skin. However unlike most amphibians this type of salamander has no lungs or gills at its adult stage.
Although amphibians have lungs, their lungs are much simpler than ours. Frogs for example don’t have a diaphragm so they must open their mouth and nostrils and essentially swallow air into their lungs. Also, although they have alveoli they have considerable less than humans.
Frogs have capillaries extremely close to the surface of their skin, since their skin is so thin, it allows for easy gas exchange with the environment. This is shown in the animation to the right.
The green layer is the epidermis (skin). Capillaries close to the surface of the skin allow for diffusion of carbon dioxide and oxygen with the environment.
Frogs use this method of respiration during hibernation.