Except when we consider intravenous feeding(, which goes through the bloodstream via an IV).Correct. And blood transfusions do not go into the stomach, which would be eating blood. Blood transfusions go intravenously, into the bloodstream. Blood into the bloodstream, food into the stomach. Two totally different things.
Moreover, one has to understand that before IVs, the way blood was "transfused" in ancient times was by mouth.