The story
From haemato- (“blood”) + -blast (“germ, sprout”). A name used in centuries past for any of various blood cells that were visible on microscopy but were not well understood at the time, all seeming like candidates for cells that might later turn into mature red or white cells. Some use of the name as referring to platelets continued even for a while after their role in clotting was apparent.
Etymology from Wiktionary, CC BY-SA 4.0.