Hello, Psychology student here, one semester away from graduation. I'm gonna give you a little primer on abnormal psychology that might help make you talking to people less weird.
First and foremost, you don't have four kinds of depression. If you have the symptoms of bipolar disorder (type 1 or 2) that includes the symptoms of major depression. Bipolar is also quite rare. If you have major depressive disorder (MDD) then you have all the symptoms of dysthymia, plus suicidal thoughts. That's honestly the only difference between the two. If you have cyclothymia then you have all the symptoms of dysthymia plus short cycles of hypomania. You cannot have even two of these, the symptoms overlap too much and the disorders are distinct.
If you need to tell others (which is a fraught process) then it helps to have an official diagnosis. Talking to strangers about your problems is scary, but especially if you have BPD you need medication. BPD is very much a brain disease and medication makes a huge difference. Medication can also really make a difference in depression symptoms.
If you're telling people generally (which is not an easy thing) just say depression. You don't need to go into details with most people (parents or intimate friends/partners might want details) so keep it broad.
For people close to you who are your support system the best thing you can tell them is how to help care for you. They don't need to know how exactly you think about killing yourself, but if you can tell them how to help you, they will appreciate it. This also makes it easier for them to hear if you combine it with ways they can help you. You get a competent support system, they get to feel less helpless in the face of your illness.
