Suicidal ideation is very simply the act of having ideas about wanting to end one's life by one's own actions. It does not necessarily relate to the frequency of such ideas, how often one has vocalized these thoughts to others, or how likely the person is to pursue those ideas into reality.
The "threat level" (as I personally call it) of suicidal ideation takes into account those factors. It also takes into account the seriousness, the intensity and the nature of the ideas themselves. One who talks about wanting to kill themselves in abstract terms, such as "I want to throw myself off a cliff" is a different level of intensity of ideation than one who has a specific cliff picked out, a means by which to hurl themselves off said cliff (such as driving their 1977 Lincoln through the guard rail and over the side of the cliff), and has worked out various details of the effort (such as stating they plan to get drunk first to get their nerve up).
Suicidal ideation is not dependent on whether or not one believes the person is at serious risk to suicide. I have been in a situation where an individual in my care made a number of wacky suicide efforts after informing me ahead of time as to what he was planning to do. He attempted to hang himself with a hand towel that wasn't long enough to even tie around his neck, stuffed crayons in his mouth and attempted to drown himself in a shallow sink without a stopper. Each time he moved extremely slowly, waiting for me to stop him. This sort of attention seeking behavior is not all that uncommon in my line of work, but it is classified as suicidal ideation and in his case had him placed on suicide watch.
A person casually mentioning to a friend, "I've been thinking about killing myself" is classified as suicidal ideation. So is the person who tells no one of his plans to drive his 1977 Lincoln through the guardrail at that hairpin curve on Hill Street. One does not have to express one's thoughts to others for there to be suicidal ideation.
Ascertaining the threat level an individual poses to themselves follows the identification of suicidal ideation in that individual. The threat level does not change the fact that suicidal ideation exists. Suicidal ideation is not an indication that a person will make an attempt to take their own life, only that the person has had ideas about doing so.