What are the two types of classification systems biologists can use to classify the animal kingdom?

Question

It is for a study guide and I am burnt out at this point can't think clearly

Answer 1

There have in recent years been three main
methods of classification: by overall resemblance, used by so-called numerical
taxonomy, by guesses at relationships, as in
the system called cladistics, and by a combination of similarity and relationship, which
was for a long time the standard method, and
still has advocates. Numerical taxonomy is
essentially extinct, though some of the computer
analyses it developed are still in use. Most
current classifications are cladistic. The use of
molecular data is still in flux. It is considered
probably more reliable than any other kind of
data, but how to interpret it is still presenting
problems. Mollecular information can be used
in either cladistic systems or in the kind that
use both relationships and similarities. Most
analyses of molecular data are still largely
dependent on overall similarity. In the final
analysis it is only by similarity that any two things
can be considered related. The differences
among the different classification systems are
in what kinds of similarity they consider relevant
to determining relationships.

Answer 2

Broad Classification:
1. Vertebrates (with a backbone)
2. Invertebrates (without a backbone)

Further Classification:
1. Porifera (sponges)
2. Cnidaria (jellyfish, hydras, sea anemones, Portuguese man-of-wars, and corals)
3. Platyhelminthes (flatworms, including planaria, flukes, and tapeworms)
4. Nematoda (roundworms, including rotifers and nematodes)
5. Mollusca (mollusks, including bivalves, snails and slugs, and octopuses and squids)
6. Annelida (segmented worms, including earthworms, leeches, and marine worms)
7. Echinodermata (including sea stars, sea cucumbers, sand dollars, and sea urchins)
8. Arthropods (including arachnids, crustaceans, millipedes, centipedes, and insects)
9. Chordata (animals with nerve chords - this group includes the vertebrates)