My layperson's understanding. I don't have any form of bipolar, so can't comment on how that is experienced, but based on my who-knows-what level of ADHD and the description Tree kindly provided of cyclothymia, I'm not really seeing the overlap. They seem unrelated as conditions (not withstanding you can have them both comorbidly). The symptoms I read in Tree's post are highly aligned to other depressive episodes - disinterest, fatigue, dulled response, suicidal ideation, etc. It is highly related to mood. The cyclical nature in common with other bipolar sees changes in these moods towards more manic states, though less than bipolar 1 or 2.
My experience of ADHD is difficulty in executive function which has a few effects. It's hard to stay on task without being distracted. There tends to be a constant feed of possibilities, ideas, tasks and other things that draw my attention which for me also means short term memories, jingles, lines from songs, people's recent words, recently heard sounds, etc. buzzing around in my head. It's hard to make good judgment calls as lots of decisions are impulsive, putting out a fire from that constant intrusion. Basically a major lack in stick-to-it-ness, impulsive behaviour (that's not impulse buying, it's just stopping something for no rhyme or reason and starting something else), trouble concentrating, impatience and an undying feeling that things aren't happening fast enough and I should be doing something else.
ETA: I guess in cases of severe ADHD and other bipolar it might look like there are overlaps. So I guess you might mistake the behaviours in a manic state with the impulsivity of ADHD, but I think the former is an expression of the mood state, whereas for ADHD it is just the executive function. And I guess the severity of the depressive state might cause a drop in motivation and so attention, but again that would be an expression of mood, whereas the ADHD is again the executive function.
Although mood affects everybody's ability to do things like concentrate or to behave impulsivity and does so too with ADHD, these things aren't dependent on mood with ADHD. So even if you're having a positive day, you still have it.