Hi, I presume you are asking for the type of names of the different definitions for 1, 2, 3 and 4. Am I right?
1. Biological definition, the most precise of all definitions, but may not be helpful to identify species that are already extinct and enshrined in stones (I.e. fossilized)
2. Morphological definition, which focuses on the morphology of animals. The thing is, some individuals with very similar morphology may be two completely different species and are unrelated.
3. Ecological definition. A niche is how an animal interacts with its environment; for e.g., how an animal gets it's food, or how it reproduces.
4. Phylogenetic definition. Sometimes it is difficult to identify the smallest group of individuals that share a common ancestor, maybe due to a lack of fossil evidence.
Hope this helps! :)