In my writing, a question like this falls within critical thinking because the philosophy of science is about inquiry. How we think. In this case, who does what is part of Idea Evaluation, one of the Five Thought Tools.
Both anthropology and paleontology explore the past. Anthropology explores our history back to the emergence of Homo habilis 2.3 million years ago. Paleontology explores the fossil record all the way back to LUCA about 3.6 billion years ago.
Anthropology focuses on the study of humans, their cultures, behaviors, and biological evolution. It includes subfields like cultural anthropology, which examines societal structures and traditions. It also includes biological anthropology, which studies human evolution and adaptation.
Paleontology, on the other hand, investigates ancient life forms through the study of fossils. All fields always overlap, paleontologists primarily examine the fossilized remains of plants, animals, and microorganisms to understand prehistoric ecosystems and the history of life on Earth.
Many fields can overlap and get blurry. Paleoanthropology draws heavily on paleontological techniques to study ancient hominins and their environments. Archaeology examines past human cultures through material remains, often intersecting with anthropology and paleontology.