It is rather subjective, but there's a few guidelines my late psychologist told me about when she diagnosed me with bipolar spectrum disorder and suggested cyclothymia:
-cyclothymia's "highs" are milder than bi-polar ones; it's a hypomania rather than mania. Mania would include delusions of grandeur (like thinking "I am God", or "I am the best, most perfect human"), very risky behavior that could possibly harm or kill you such as dangerous drug use or sexual activity, being disconnected from reality and feeling invincible, etc. Whereas hypomania would be like feeling really good and energetic for no reason, being more productive, and possibly doing risky behavior, but to a lesser extent than full-blown mania. The key difference, she said, was that if you have a full manic episode you often end up either in hospital, mental institution, or jail. Basically, you get yourself in some big trouble. Manic episodes are the "classic" signs of bi-polar disorder, so the difference between cyclothymic and bi-polar manic episodes are generally the main thing that psychologists will look at in determining which one you have, if either.
-cyclothymia episode cycling is different. Bi-polar cycles tend to be more spread out and last longer, while cyclothymia tends to be more "rapid" cycling. This is different for everyone, though.
-cyclothymic depressive episodes
can involve major depression, unlike what another poster said (I've had major depressive episodes but no full mania). With cyclothymia there tends to be a constant, mild depression that's interrupted by periods of hypomania and then heavier-than-usual depression.
Bi-polarity is a spectrum and cyclothymia is just another classification within that spectrum. The specifics are different for everyone. Some might be cyclothymic with less severe depression than others, some might be bi-polar with less severe mania than others. And the depressive and manic episodes can manifest differently for everyone. Some people who are depressed might find it hard to find the strength or motivation to practice daily hygiene but still have the will to socialize, while others might be able to still shower regularly but become more reclusive. The diagnosis is tricky, and comorbid conditions can complicate it. Some psychologists might just diagnose you with bipolar spectrum disorder rather than "Bipolar II" or "cyclothymia", because it can be hard to judge where one ends and the other begins. The important thing is mainly to know whether you're on the spectrum or not, because, if you are, then you will react differently to meds like anti-depressants than someone who has unipolar depression--if you're taking anti-depressants to treat depression in and are unknowingly on the bipolar spectrum, it could trigger and exacerbate a manic/hypomanic episode, or simply not treat the depression. So if you think you experience mania of any severity it would be important to get a diagnosis before taking certain meds. Also, cyclothymia left unchecked and untreated can worsen and the hypomania could potentially become full mania and the depressive episodes could be subsequently heavier as well.
If all this wasn't complicated enough, you can be on the bipolar spectrum and show almost no signs of mania at all--yet you would still react differently to meds than someone who is unipolar would. Think of it like a line graph, with Time on the x-axis and Mood on the y-axis; someone who is unipolar would have a roughly straight line throughout time, not including external factors like the death of a loved one or something that would make it temporarily plummit. Someone who is on the bipolar spectrum would have a pattern of their Mood curve going up (how high it goes depends on the severity of mania one experiences), then down following the manic episode, into the depression "crash" (like a sugar high leads into a sugar low), then this line will go back up to a "baseline" mood that can either be above, below, or at the average neurotypical mood level. This cycle will repeat. Those with cyclothymia tend to experience this cycle more often in the same amount of time, and tend to have their "baseline" mood a little lower than average, and their curve won't go as high as someone who has full mania (and in some people it might barely go up, which makes it harder to notice/diagnose), but their downward curve can go rather low, and one may experience major depressive episodes (at least according to my psychologist last year). That's it as succinctly as I can put it