What are set of words word like "crocodiles" and "alligators", and "turtle" and "tortoise" called?

Solution 1:

These are prototypes in the language of taxonomy.

In many sciences, from pathology to taxonomy, prototype refers to a disease, species, etc. which sets a good example for the whole category.

https://en.wikipedia.org/wiki/Prototype

Another term is archetype, but it tends to be a more formal designation, something like a prototype with credentials.

They are not, as has been pointed out, synonyms, nor are they misnomers.

A more general idea is pars pro toto, where a part is used to refer to the whole. A mereism is a list of parts intended to substitute for the whole. Thus the sets are mereisms for the clades that contain them. Unfortunately, mereism has a particular meaning in biology, and would be confusing if used this way here.

Solution 2:

umbrella term (or) blanket term

Is I think what the OP is after. A word that covers many different, but closely related things. For example, an American might refer to a crocodile as an alligator because they might be more familiar with that species of semiaquatic reptile. Someone from the southern states of the US might call Norwegian lobsters, langoustine, scampi, or prawns as crayfish (source) because they seem to belong to the same genus. It's quicker to say, and remember

Twenty years ago, I remember hearing children call tortoises, turtles because of the popular 1980s cartoon series, Ninja Turtles.

An umbrella term is a word or phrase that covers a wide range of concepts belonging to a common category. For example, cryptology is an umbrella term that encompasses cryptography and cryptanalysis, among other fields.

A blanket term is a closely related word or phrase that is used to describe multiple groups of related things.

• The degree of relation may vary or have a minimal relationship, but blanket terms often trade specificity for ease of use.
• In other words, a blanket term, by itself, gives little detail about the things that it describes or the relationships between them, but it is easy to say and remember.

Wikipedia