When you receive stem cells donated from other people, your body knows the difference. Immune systems are trained to attack and destroy "foreign" (not from your body) proteins, whether they are bacteria, viruses, cancer cells or transplanted tissues. The differences between your body's and the donor's cells lead to a fight and attempts of one to destroy the other.
Sometimes, the healthy donor stem cells recognize the patient's tissues as foreign and attack them. This is the "transplant against the patient," or "Graft versus Host Disease" (GvHD).
Commonly, Graft versus Host Disease is divided into acute GvHD and chronic GvHD.
Acute Graft versus Host Disease can lead to chronic GvHD, but chronic GvHD may occur without any evidence of previous acute GvHD.