With normal Bipolar Disorder, a patient will have periods of stable mood in-between episodes of (hypo)mania and depression.

"Rapid Cycling bipolar disorder is often diagnosed when a patient has four or more mood episodes during a 12-month period. This essentially means that an individual with rapid cycling bipolar disorder can constantly cycle between periods of (hypo)mania and depression, without any periods of stable mood in between each episode. In fact – that’s the criteria of a rapid cycling bipolar disorder diagnoses (under DSM-IV).

Ultra Rapid Cycling bipolar disorder is rather rare. It’s a lot like rapid cycling, except ultra rapid cycling patients can experience multiple periods of hypomania and depression each day. A patient experiencing ultra rapid cycling will not have any period of ‘normal mood’ between the many cycles they experience throughout the day. The understanding of this type of bipolar disorder is still being researched and is still debated by those in the psychiatry industry.

Cyclothamia is part of the Bipolar spectrum and is characterised by frequent changes in mood and cycles between hypomania and mild to moderate depression. It is thought that those with Cyclothamia experience episodes in a lower severity than those of Bipolar I and Bipolar II. Unlike rapid cycling and indeed ultra rapid cycling, Cyclothamia is a diagnoses in itself – the prior two are actually just used in conjunction with a Bipolar I or Bipolar II diagnoses. Despite the lower severity of individual episodes, Cyclothamia can be devastating to someone’s life purely because of the frequency of mood cycles."

Taken from my blog.

I also need to add that ultra ultra rapid cycling (Ultradian) Bipolar can mean multiple episodes in a single day, whereas Ultra Rapid Cycling could be slightly more infrequent, with a change in state after a matter of days.

Hope that helps!
RB.