The concept of "suicidal thoughts" and "suicidal intention" is one that has caused me a lot of grief. I presented to a psychiatrist and said I had frequent suicidal thoughts - and I was sent to a partial hospital program pretty much against my will, by which I mean I was afraid to say "no" lest something worse happen. And even the PHP was a compromise, I was first ordered to go to the ER and admit myself, which I did absolutely refuse to do ... all of that as background.
The thing that psychiatrist wouldn't acknowledge was that I said, very truthfully, that I had many thoughts of suicide, pretty vivid ones in fact, like a movie in my head, and a feeling of "how it would be" - but I had no plan at that time to actually follow through with it - in fact, the opposite, I stated, agian truthfully, that I couldn't live like that any more, again misinterpreted to mean I was going to kill myself, even though I explained it meant I wanted help to have a better, happier life.
So, yes, I had a bad experience in that sense with suicidal thoughts .. .and it colored my subsequent interactions with mental health professionals for a while. But I did go into a couple of depressions when they recurred ... and finally, I got very brave with my current psychiatrist, after getting to know her reasonably well, believe she was genuinely very competent and helpful and kind, and that she would not overreact ... and she didn't. In fact, she said something along the lines of "suicidal thoughts are just a symptom ... they are not dangerous until they lead to the intent phase". It made me feel a lot better. Furthermore, she said it was something to work with in terms of pharmacology and therapy, not something in and of itself to fear to a great extent. Only if you start planning ... then worry.
So, if you are planning, like acquiring the means, decididing on the when and where, that kind of thing, then worry, or even push the panic button it it is imminent.
If you are just seeing visions of it in your head, or having feelings or general thoughts like "I wish I were dead" ... then realize it is a sign that you need to do something, but that you can overcome it. Still worry, probably yes, but ... I think of it this way, it's the difference between severing a major artery and severing a smaller vein - one is imminently dangerous, the other is painful, messy, but not going to kill you any time soon.
I hope this makes sense, and I'm not trying to diminish the severity of either ST or SI, but ... it was a revelation and like "fresh air" to me to know that having those feelings wasn't an automatic trip to the locked ward or whatever, that it is something a good professional can help you manage and minimize or overcome.
Hope that helps.