I thought I would get that point across. You would not be incorrect by referring to every tailless amphibian as a frog. True toads are of the genus Bufo, such as a fowler's or a cane toad. Others are not true toads, such as spadefoots, and I am hearing more professionals refer to them as "spadefoot frogs".
Lets look at it this way. Everyone in Virginia is in the United States, not everyone on the US is in VA. Every toad is a frog, but they really are all frogs!
Along the same lines, all newts are salamanders. Turtles are worse, since it almost subjective what we call turtle, tortoise or terrapin, but they are all turtles.
A good discussion is linked below
Link
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...the oldest task in human history: to live on a piece of land without spoiling it."
Aldo Leopold (1938)
"Sometimes I think the surest sign that intelligent life exists elsewhere in the universe is that none of it has tried to contact us."
Calvin and Hobbes (Scientific Progress Goes 'Boink', 1991)