Archaeology is a branch or sub-field of anthropology. Branches of archaeology are really specific areas in which an archaeologist focuses. Therefore since the 1970s more and more archaeologists are focusing in one area of archaeology.
There are two main branches of archaeology, which are historical archaeology and forensic archaeology. But all fields of archaeology study materials. The materials are rocks, fossils, pottery or ceramics, garbage, bones, etc. Anything that represents an object can be studied, catalogued, and researched by the archaeologist.
The fields of archaeology overlap depending on the type of study done. Such as a branch of archaeology could be museums where archaeological objects are stored, displayed, catalogued and taken care of.
Archaeologists might focus on one particular dig such a dig in Mesoamerica or Egypt. An archaeologist who does most his work in Egypt could be working in the archaeological field of Egyptology. Archaeologists focusing on US archaeology could be said to be working in a branch of archaeology called American archaeology, which would include the study of North America, US, Canada, South America, and Central America (Mesoamerica). An archaeologist could focus totally on any of these geographic areas such as focusing entirely on the Mayan culture in Mesoamerica.
Historical archaeology would include classical archaeology and pre-historical archaeology. and many other types of archaeology.
Paleontology is often thought of as a branch of archaeology, but is really a separate science, since it is concerned mainly with the study of the dinosaurs and evolution before true humans existed. However, paleontology uses many elements of archaeology and also studies materials such as bones, skulls, and tools.
Since archaeology is a branch of anthropology, which mainly studies humans as primates. it is therefore a social science; whereas paleontology is an earth science.
Forensics archaeology has become a very important science today and deals only with the bones, teeth, and skulls of humans who died an unnatural death. Forensics archaeology would work closely with criminologists and law enforcement to uncover DNA findings that can lead to the apprehension of people involved in criminal activity such as murder.
All other archaeology deals with the historical approach to archaeology, but however there are many different fields to work in and the fields are increasing as more people become involved in archaeological study.
According to allexperts.com, archaeologists might work in these areas: paleo-botany, osteology, limnology, archaeological geology, ceramics, archaeological engineering; or Egyptology, Native American studies, Ancient Chinese studies, lithics (ancient tools), ancient metallurgy, structural engineering, or pre-historic archaeology.
The following types of archaeology are studied according to greatarchaeology.com: African, American, computational, battlefield, classical, environmental, ethno, European, experimental, historic, forensic, industrial, maritime or underwater, medieval, Near Eastern, landscape, Post Medieval, Prehistoric, Pro Historic, urban, and Australian archaeology. Also, archaeoastronomy, archaeobotany archaeometry, archaeozoology, assiriology, calceology, Egyptology, osteology, Pheniciology, and Taphonomy. To learn more about these sub-fields of archaeology you can go to greatarchaeology.com where there is an explanation of each sub-field.
In all cases here, archaeology is studied the same way, by the identification of materials and objects; and by using the scientific method. Archaeology is a branch of anthropology, which seeks to determine how primates (mainly human primates) lived within their cultures. Therefore archaeology helps the anthropologist determine ways and mores of a culture through the materials found by the archaeologist. Also, an archaeologist is also an anthropologist.
Archaeologists "...explain topics such as the emergence of agriculture, the evolution of technology, the appearance of complex societies, and how societies change over long periods of time."
Therefore, archaeology is a branch of anthropology that helps anthropologists study a particular culture; and the branches of archaeology are specific areas studied by anthropologists.