Legend has it that, once upon a time, a Spaniard landed in Germany with an unsettled stomach and walked into a café to get a comforting tea. And then false friends happened.
From Latin īnfundō (to pour in, upon or into), an infusion originally referred to the liquid which had had ingredients steeped in it to extract useful qualities, hence nowadays we still use the word infusion for beverages such as tea. Later on the term slid into medicine to refer to the administration of liquid substances directly into a vein, i.e. transfusion. False friends may not as distant as they might seem. One just has to find the etymological link between them. : )