As you can see, there are several different variations to the rhyme. All of them ONLY apply to The Southeastern U.S. and they ONLY refer to the coral snake (venomous), with red and yellow bands touching, in opposition to the scarlet snake and scarlet king snake (both non-venomous), where the red and yellow bands don't touch, (the scarlet snake often has white bands intsead of yellow).
This rhyme doesn't work for any other venomous snakes in that region, (all vipers) such as water moccasins, copperheads, and rattlesnakes. And the rhyme doesn't apply in the western U.S. at all.
A coral snake is not a viper, so it may look quite harmless as it has a small head. A black nose is a good indicator while the other two mentioned above have red noses. Coral snakes look more similar to the scarlet king, as the bands wrap all the way around the body, with the scarlet snake the bands or 'saddles only reach the belly, which is usually a creamy white color.
Thirty-seven years of wild and domestic snake handling and observation.