> comparaison of suicide rates between countries is,

Go careful, a lot of them count deaths in very different ways. Some of them even change the way they count death, and so you need to be careful if you're comparing rates across time for one country.

In the UK:

> The previous National Statistics definition of suicide includes deaths from intentional self-harm (where a coroner has given a suicide conclusion or made it clear in the narrative conclusion that the deceased intended to kill themselves) and events of undetermined intent (mainly deaths where a coroner has given an open conclusion) in people aged 15 and over.

[...]

> In 2016, the suicide definition was revised to include deaths from intentional self-harm in children aged 10 to 14. Previously we did not include suicides in young children due to the very small numbers involved (see Table 3). However, after discussions with Public Health England and the constituent countries of the UK, it was decided that it was appropriate to include them. Deaths from an event of undetermined intent in 10- to- 14-year-olds are not included in these suicide statistics, because although for older teenagers and adults we assume that in these deaths the harm was self-inflicted, for younger children it is not clear whether this assumption is appropriate.

So, death after self harm, even if there's no evidence of intent to die.

In the US: https://www.cdc.gov/violenceprevention/pdf/Self-Directed-Vio...

> Suicide

> Death caused by self-directed injurious behavior with any intent to die as a result of the behavior.

But it's a bit more complicated:

> Despite the large volume of data on certain types of SDV, the utility and reproducibility of the resulting information is sometimes questionable. Mortality data are problematic for several reasons: geographical differences in the definition of suicide and how equivocal cases are classified; jurisdictional differences in the requirements for the office of coroner or medical examiner affecting the standard of proof required to classify a death as a suicide; and differences in terms of the extent to which potential suicides are investigated to accurately determine cause of death.18

https://www.cdc.gov/violenceprevention/pdf/suicideTechnicalP...

> Gathering ongoing and systematic data is important for prevention efforts. However, it is also important to gather data that are uniform and consistent across systems. Consistent data allow public health and other entities to better gauge the scope of the problem, identify high-risk groups, and monitor the effects of prevention programs and policies. Currently, it is common for different sectors, agencies, and organizations to employ varying definitions of suicidal ideation, behavior, and death that can make it difficult to consistently monitor specific outcomes across sectors and over time. For example, the manner in which deaths are classified can change from one jurisdiction to another, and can change based on local medical and/or medico-legal standards.4 CDC’s uniform definitions and recommended data elements for self-directed violence provide a useful framework to help ensure that data are collected in a consistent manner across surveillance systems.

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