The variety of days set aside to remember the Holocaust is part of its story.
The Holocaust was not the only case of genocide in history, and perhaps not the most thorough in the sense that something like two-thirds of the Jews were not killed, and the remnant has gone on to considerable success. Nonetheless, the Holocaust stands out as the work of a nation advanced by all measures of economics and culture, it was perpetrated in a sophisticated manner rather than being the work of ragged gangs or out of control soldiers. Moreover, it was directed against a population that was not in armed opposition to the government that marked it for extermination. 
Israel''s official commemoration of the Holocaust this year begins in the evening of May 1st. The timing is linked to the celebration of Independence Day on the fifth of Iyar (this year beginning in the evening of May 9th). Holocaust Memorial Day occurs a week and one day before Independence Day, and a week before the Memorial Day that commemorates Israelis who died in defense of the country or as the result of terror. For some time before each of those days, the media focuses on tragedies, and the heroism of those who resisted the Holocaust or participated in Israel''s security forces. Holocaust survivors have largely passed from the scene. This year the media are emphasizing how many are dying on an average day and how many remain alive, and giving increased attention of the memories held by descendants.
Israel Independence Day occurs immediately after those two Memorial days. It is a day for celebrating life and accomplishment.
The United Nations and numerous countries commemorate the Holocaust on January 27th, the date of liberation in 1945 of Auschwitz-Birkenau. A number of congregations commemorate the Holocaust on the 9th of Av (Tisha B''Av), chosen on account of its association with several tragic events in history, beginning with the destruction of the Temple by the Babylonians in 586 BCE. Some remember the Holocaust on the tenth of Tevet (prior to Hanukah), the day set aside to remember the onset of the Babylonian siege of Jerusalem. While numerous ultra-Orthodox observe two minutes of stopping their cars, standing still, and silence when Israel''s sirens sound in the morning of Holocaust Day, other ultra-Orthodox continue at their activity in defiance of what they view as an improper observance by the secular state.
Other variations reflect definitions of who suffered from the Holocaust, and the compensation due to them.
Jews of German origin have done better than others.  West Germany agreed in 1952 to pay reparations to individuals, and collectively to the State of Israel for those who could not be identified, on account of death, slave labor, other persecution, and for property stolen by the Nazis. Over the years the payments have provided substantial resources to Jews who had suffered as Germans, and capital that Israel devoted to its infrastructure of public transportation and other public services. The reparations were also an element in Germany''s return to the list of countries recognized as worthy. 
Individual cases have involved deliberations about entitlement and amounts. In regard to compensation for property seized, there have been disputes about claims of ownership, valuation, and whether amounts paid by Germans in the 1930s were substantially below market value and represented the exploitation of Jews concerned for their lives.
Jews who suffered from the Nazis or their collaborators in other countries have been less fortunate. National governments have claimed limited responsibility due to being occupied by the Germans, or being unable to afford the payments. Googling "Holocaust compensation" produces almost 2.7 million items.
The collapse of the Soviet Union and the migration of a million and one-half Jews to Israel and elsewhere began a series of claims on behalf of individuals who had been prevented by Cold War politics from presenting their demands. Most recently, Moroccan Jews have won recognition as Holocaust survivors. The German and Israeli governments have been pressured to compensate a continuing series of new claimants. Individual Israelis ponder the benefits that ought to be paid to individuals defined as Holocaust survivors due to personal suffering or their residence in countries occupied by the Nazis, as opposed to needy individuals no matter what the source of their problems. Moroccan Jews who qualify as having suffered Nazi persecution will receive 13,000 shekels from the German government (the equivalent of US $3,800).
Banks and insurance companies in Switzerland, Italy, Israel and elsewhere have been charged with being insensitive or worse with respect to procedures used for claims about deposits or death benefits. The government of Poland has admitted responsibility for property seized from Jews, but has indicated that it does not have the resources to pay claimants. 
Ha''aretz has a front page story about competition between various organizations representing Holocaust survivors, their inability to agree on a format for a meeting designed to coordinate their efforts, or a joint announcement after their meeting. 
Among the issues are continuing demands for compensation on account of seized property. There are outstanding claims for homes, art work, businesses, and other assets. Organizations and politicians keep support their cases with occasional campaigns. Other voices ask about the compensation of Palestinians for property seized by the State of Israel in 1948. We hear that Holocaust claimants are in a distinct class because they were innocent civilians, while Palestinians participated in armed combat. We also hear that Justice is elusive, especially when it involves memories from the 1930s and 1940s, and that it might be wise to weigh our demands about revisiting history.