How do scientists group living things as plants or animals?

Answer 1

By their characteristics.

Generally animals are capable of spontaneous movement, they ingest food to digest it and they lack rigid cell walls (unlike plants). Please see the link.

Answer 2

Scientists group living things as plants or animals based on their fundamental characteristics, such as how they obtain nutrients (autotroph or heterotroph), cell structure (eukaryotic or prokaryotic), and mode of reproduction. These distinctions help categorize organisms into kingdoms, such as Plantae or Animalia.