Aren't all suicidal people crazy?

No.

Having suicidal thoughts does not imply that you are crazy, or necessarily mentally ill. People who attempt suicide are often acutely distressed and the vast majority are depressed to some extent. This depression may be either a reactive depression which is an entirely normal reaction to difficult circumstances, or may be an endogenous depression which is the result of a diagnosable mental illness with other underlying causes. It may also be a combination of the two.

The question of mental illness is a difficult one because both these kinds of depression may have similar symptoms and effects. Furthermore, the exact definition of depression as a diagnosable mental illnesses (i.e. clinical depression) tends to be somewhat fluid and inexact, so whether a person who is distressed enough to attempt suicide would be diagnosed as suffering from clinical depression may vary in different peoples opinions, and may also vary between cultures.

It's more helpful to distinguish between these two types of depression and treat each accordingly than to diagnose all such depression as being a form of mental illness, even though a person suffering from a reactive depression might match the diagnostic criteria typically used to diagnose clinical depression. For example, Appleby and Condonis write:
"The majority of individuals who commit suicide do not have a diagnosable mental illness. They are people just like you and I who at a particular time are feeling isolated, desperately unhappy and alone. Suicidal thoughts and actions may be the result of life's stresses and losses. The individual can feel that they just can't cope any more.

In a society where there is much stigma and ignorance regarding mental illness, a person who feels suicidal may fear that other people will think they are "crazy" if they tell them how they feel, and so may be reluctant to reach out for help in a crisis. In any case, describing someone as "crazy", which has strong negative connotations, probably isn't helpful and is more likely to dissuade someone from seeking help which may be very beneficial, whether they have a diagnosable mental illness or not."

People who are suffering from a mental illness, such as schizophrenia or clinical depression, do have significantly higher suicide rates than average, although they are still in the minority of attemptors. For these people, having their illness correctly diagnosed can mean that an appropriate treatment can begin to address it.