Both of these careers are similar, but with a different focus.
A forensic anthropologist is someone who would be able to look at human remains that are either badly decomposed, skeletal, or damaged and discover information about that person. They may be able to tell sex, height, weight, disease, race, and discover other evidence of how the person died. This information is used in an attempt to identify unknown victims. Information from a forensic anthropologist can even be used to make models of faces based on skulls. A fictional example would be that lady on the TV show Bones (though, in the show, she really acts as both.)
A medical examiner is someone who performs autopsies in an effort to determine a cause of death. If someone dies of unknown causes, or if the death is suspicious in some way, the medical examiner will attempt to find out exactly what killed him or her. A fictional example would be that old guy with the cane from CSI.
Both of these jobs are concerned with dead folks, and both are used in court cases to provide testimony. The real difference is that an FA mainly attempts to identify whose remains have been found, while a ME tries to determine what specifically killed them. Though both jobs might have some skills relating to the other, it isn't their specialty.