What would happen if I told my therapist I experience suicidal thoughts?

I'm not suicidal. Being suicidal means you want to die and you have actual plans to kill yourself, right? Well, I don't want to die and I'm not planning on doing so. However, I think about it quite a bit. I get thoughts like "perhaps you should just kill yourself", "why are you even alive? Things won't get better anyway", "I hate my life" etc. I also get sudden thoughts (they're like flashes) like "perhaps you should just throw yourself out the window", "perhaps you should just jump out on the street in front of all those cars", "bleach? Drink it!", "a nail? Perhaps you should just push it into your eye and see what happens" and things like that. Even though I don't want to go through with them the thoughts sometimes scare me a little bit. What if I get really impulsive and do something stupid? I mostly get these thoughts when I'm in one of my very low episodes or when I'm anxious about failing things (studies for example).

Are these really suicidal thoughts? What would happen if I told my therapist about them? Should I tell him? Is it important? Would the thoughts be taken seriously? I feel like I'm approaching one of those episodes of extremely low mood (they usually last for a few weeks/a month before going back to my "normal depression"). Maybe I'm already there. Anyway, that means the thoughts are back. Hence me asking all those questions (I hope it's ok to ask questions like these in this forum).

Thanks (also, sorry if I'm posting too much).