The process in which a relatively unspecialized cell acquires the characteristics of a mature hemangioblast. Hemangioblasts are the proposed common precursor of blood and endothelial lineages. [ http://www.ncbi.nlm.nih.gov/pubmed/9670018 GOC:bf http://www.ncbi.nlm.nih.gov/pubmed/15378083 GOC:dph ]