More from Michael Inwood's dictionary on events in Being and Time.
In BT Ereignis is still used for an event that happens to me. It can apply to 'a storm, refurbishing one's house or the arrival of a friend, hence to things that are present-at-hand, ready-to-hand or there-with-us' (BT, 250). Vorkommnis and vorkommen are usually reserved for the vorhanden, the present-at-hand' (cf BT, 119). Words beginning with vor- are often associated with the present-at-hand and the theoretical, objectifying attitude, as when 'coming across oneself' [Sich-vorfinden] perceptually' is contrasted with 'finding oneself in a mood [gestimmtes Sichbefinden]' (BT, 135). But this does not apply when vor- has a temporal force, whether of anticipation, e.g. vorweg, 'ahead', or of antecedence, e.g. vorgängig, 'previous(ly)'. The most potent word for 'happening' in BT is (das) Geschehen, which Heidegger associates with its relative Geschichte, 'history'. Geschehen is understood verbally as 'happening', not as an individual 'event'. It is thus quite distinct from Geschehnis, which occurs only twice in BT, to distinguish the 'processes [Vorgänge] of nature and the events [Geschehnisse] of history (18) and to refer to not fully theoretical 'assertions about events in the world around us' (158). A burst pipe or car crash are Geschehnisse, but not Geschehen: only Dasein 'happens'. Dasein's happening is the 'specific movement in which Dasein is stretched along and stretches itself along' between its birth and its death (BT, 375). Exploration of this shows us how Dasein 'pulls itself together' into a unified self and thereby gives rise to history: "Or does the personality of the person, the humanity of the man, have its own temporality and correspondingly a "steadfastness" of its own, in virtue of which too the Geschehen-character of man's Dasein, i.e. the essence of history in the authentic sense, determines itself in a radically different way from the Vorgang-character of present-at-hand nature? (XXXI, 173). Dasein is a happening, not a substance in and to which various things happen. In pulling itself together it 'repeats" or retrieves the historical past.
