Why aren't intermittent fasting plans complete fasts?

Fasting for a whole day is one approach to intermittent fasting, if you want to do it that way. But there are various approaches, as you've read about. It's not like this sort of thing is regulated by law.

The point is to get some extended period of time without spiking your blood sugar, and instead trying to get your body into full-on fat-burning mode. I think the point is you don't HAVE to fast an entire calendar day if you don't want to.

Early research on intermittent fasting (http://www.ncbi.nlm.nih.gov/pubmed/5936189 -- 1966; http://www.ncbi.nlm.nih.gov/pubmed/1029820 -- 1976) found that complete fasting was unhealthy and very, very difficult to maintain - hunger, weakness and emotional imbalance (anger, depression.)

In the early 2000's, church-style fasting was found to be an important component of the Mediterranean Diet (1500-2000 years of Greek Orthodox, Roman Catholic tradition - one small meal, or two snacks and one tiny meal -- http://www.ncbi.nlm.nih.gov/pubmed/12753698 -- 2003; http://www.ncbi.nlm.nih.gov/pubmed/18093353 -- 2008)

Recently, researchers such as Harvie, Varady, Johnson, Klempel and others have found that even with some food, retention in intermittent fasting clinical trials is only around 90%: many people simply cannot deal with the physical effects. However, with the addition of a small amount of calories on fasting days, the extremely negative effects of complete fasting were ameliorated, if not eliminated.

So - two reasons: many humans react poorly to fasting, and the traditional western fast included some calories. Other fasting traditions, such as Ramadan, also incorporated some food.