Word for "moving up one conceptual level"
Solution 1:
Your question relates to the concepts of hyponymy and hypernymy, which describe the specific-to-general relationships that your examples illustrate. We can think of branching trees of examples or subordinate ideas, with general or superordinate concepts at the top and more specific concepts branching out below.
Hyponymy / hypernymy demonstrates "type of" relationships, aka to the computer scientist as "is-a relationships."
In your first example, bats and rats are hyponyms of the hypernym "mammal." In turn, mammal, along with marsupial and reptile, are hyponyms of the hypernym "animal." You could take "bat" as a hypernym and branch down with the hyponyms megabat and microbat. And so on.
The same relationships apply to your other examples as well.
One important use of hypernyms is in noun definitions, as in: an X is a Y that... or X is a Y of..., in which X is a hyponym and Y is a hypernym of X.
Solution 2:
One possible term is level of abstraction. Each level you move up has less specific detail and more general characteristics of the group or groups.