Forensic science could be described as the practical application of science in the service of the Law.
Forensic Sciences host a large group of diverse fields of expertise, ranging from forensic anthropology to ballistics, fingerprints (dactyloscopy), DNA analysis, odontology, bloodstain pattern analysis, trace evidence and forensic document examination.
Forensic Document Examination is the forensic discipline that focuses on the analysis of disputed documents, examining the handwriting/signature authorship, the obliterations/erasures in the document, the ink and the writing instruments, the safety features etc.
Handwriting seen through the scope of Forensic Document Examination is an acquired perceptual-motor task, of high complexity. Handwriting identification is a discriminatory process based on comparison of different handwriting groups which aims to investigate whether the writer x has written the y handwriting or signature sample (zero hypothesis) or not (alternative hypothesis).
No. A forensic document examiner (FDE) could also examine printings, banknotes, rubber stamps, inks, paper, photocopies, computer, typewriter generated documents and many more. This expert had worked on a case in which the graffiti on a wall was examined.
No. An (analytical) graphologist professes to do this. Forensic Document Examiners are not graphologists and vice versa.
You can find more details regarding the discipline of Forensic Document Examination here