The difference is substantial.
The government says there have been 2,629 murders. The Observatorio de Violencia recorded 3,547 homicides during the same period.
The government says there isn't paperwork or bodies to substantiate 918 homicides counted by the Observatorio. The Observatorio says it has paperwork and bodies for all of them, and that it got that information from the same government sources the Minister of Security and Defense, Arturo Corrales, says don't have them.
There is an explanation.
Corrales admits that when he was appointed, he ordered a change in the methodology of the way homicides were counted, applying a new Sistema Regional de Indicadores Estandardizados de Convivencia y Seguridad Ciudadana (Standard Indicators of Living Together and Citizen Security), promulgated by the Banco Interamericano de Desarrollo (BID). This is a way of standardizing social statistics, including the measure of homicides, between countries to allow comparison. This new protocol to standardize how countries report crime statistics is described in an article (linked above) published in the 2012 edition of the Revista Panamericana de Salud Publica.
So Corrales asserts that the difference in count is because the Observatorio de Violencia is not following the proper methodology. For Corrales to count a death as murder, he requires both that there be an autopsy, and a coroner's report calling the death homicide. Corrales says that those 918 cases are only "possible homicides" because either they lack the body, or the coroner's report declaring it a homicide.
Reality check: coroners work in, and autopsies are only performed, in Tegucigalpa, La Ceiba, and San Pedro Sula. Many families do not allow autopsies to be performed, reclaiming the body for burial almost immediately. Thus any statistic that requires both an autopsy and coroner's report will significantly undercount homicides in Honduras.
The Observatorio de Violencia has been following internationally recognized procedures since 2004, using the same approach to accumulate data from the national police and the investigative police, as well as the coroners.
Migdonia Ayestas, the Observatorio de Violencia coordinator, said of Corrales:
If the Secretary of Security does not incorporate all the homicides attested to in his files, there is a problem with his analysis. The police report says "dead", says by firearm, and gives a name and surname.
Of the 918 disputed cases, all have a police report; 786 of them have a cause of death indicated in the report; and only 135 lack the name of the individual. Ayestas says there are about 400 cases where the police have not declared the death a homicide, and that the Observatorio does not count those cases.
Why is this a problem? Changing methods impedes assessing trends over time.
Corrales wants to assert that the current homicide rate in Honduras has fallen dramatically, to 70 per 100,000 population from the reported 85-91 per 100,000 in 2012. The Observatorio de Violencia agrees that the homicide rate has fallen slightly, to about 80 per 100,000. The difference is that the Observatorio de Violencia is comparing two numbers calculated the same way; Corrales has changed the rules, so really we cannot compare the 2012 and 2013 numbers. One way the murder rate fell about 18-23%; the way the Observatorio has always used, by 6-12%.
The takeaway here is that the government is no longer following the same procedures it was following for counting murders, and therefore the numbers it gives out from now on will be incommensurate with the homicide rates it reported before. The Observatorio de Violencia is following the same procedures, so its current and past numbers will be comparable.
Or, put another way, Corrales is prepared to change the way he counts homicides so that it looks like the Lobo Sosa government is being much more effective against crime than it really is. To do so he invented a methodology that because of how things work in Honduras, will significantly undercount the homicide rate.