barking frog vs toad frog

barking frog and toad frog both are nouns.

Word	Noun	Adjective	Verb	Adverb
barking frog	Yes	No	No	No
toad frog	Yes	No	No	No

As nouns, toad frog is a hypernym of barking frog; that is, toad frog is a word with a broader meaning than barking frog:

barking frog: of southwest United States and Mexico; call is like a dog's bark
toad frog: any of various tailless stout-bodied amphibians with long hind limbs for leaping; semiaquatic and terrestrial species

Other hypernyms of barking frog include anuran, batrachian, frog, salientian, toad.

barking frog (noun)	toad frog (noun)
of southwest United States and Mexico; call is like a dog's bark	any of various tailless stout-bodied amphibians with long hind limbs for leaping; semiaquatic and terrestrial species