I think two of the first replies taken together are helpful:
Kilaya: Wrathful Vajrasattva, Karma or Vajra Family, focus of practice is eliminating obstacles through wrathful means, esp. purification of anger and negative karma.
Dorje Drollo: Wrathful Guru Rinpoche (the form in which he concealed many of his Termas), Pema Family, focus of practice is elimination of obstacles through crazy wisdom, also through subduing demonic forces (Dud-dul).
I know this is a long post, but maybe the following is of interest to someone. If I am incorrect on anything here, someone please correct me!
Kilaya Tantras originate from the Oddiyana Dakini Lekyi Wangmo, to Prabahasti (one of the Eight Vidyadharas of India) and on to Guru Rinpoche, and thus are both Kama and Terma.
Dorje Drollo I believe is mostly, if not exclusively a Terma practice (if it is even possible for that to be the case).
Vajrakilaya practice is extremely common in Nyingma monasteries as an extensive Drupchen prior to Losar to remove obstacles for the coming year (and presumably to purify negative karma from the past year?) As far as I know Drollo is not as universally an annual practice, though in some lineages and western Dharma centers it is. At Palyul Namdroling Monastery in S. India, there is a temple dedicated entirely to Vajrakilaya. I have fond memories of the monks in the temple pounding the drums and metal khangling horns shredding through the morning air like a crazed swarm of mutant bees in a lightning storm. Terrifying and comforting at the same time (terrifying to my ego and comforting to my buddhanature perhaps?). This was a common puja performed not only in the Drupchen, but whenever it was requested by a sponsor and maybe on the 29th day of each month (also common to do with protectors on that day). I also recently had a very powerful experience after doing a single concise Vajrakilaya practice that convinced me of the power of that deity to remove obstacles. If you feel you would benefit from hearing the story, I feel there would be no fault in sharing it (no meditative realizations or anything like that, but eerily significant events around it). Also witnessed an amazing display at a Vajrakilaya empowerment with H.H. Penor Rinpoche in Pharping, Nepal in 2005.
At the Pema Osel Ling retreat center of Lama Tharchin and H.H. Dungse Thinley Norbu Rinpoche in California there is a Dudul Chorten (basically a Dorje Drollo Stupa). Also the 50 ft. Zuni Mountain Stupa is a Dudul Chorten in N.W. New Mexico but in a different architectural style. Both contain thousands of Dorje Drollo Tsa Tsas inside the vase in order to pacify negative forces in the degenerate age.
Zuni Mountain Stupa, NM
Dorje Drollo Stupa at P.O.L., CA
My lama Bhakha Rinpoche
, a Dudjom lineage holder who served Dudjom Rinpoche closely for many years, has imparted the following about Dorje Drolö practice: The wrathful practice of Dorje Drolö is critically important in pacifying all the negative circumstances that we face in today's world. Since the whole spectrum of Buddhadharma teachings and its essence is love, compassion, and wisdom, this wrathful practice is not just the expression of some sort of ordinary rage; rather, it is the pinnacle practice of compassion and wisdom underlying the practice of Buddhadharma at its most profound level. Therefore, for the sake of all sentient beings, particularly in this degenerate time, this practice is a very powerful and immediately effective way of bringing peace and harmony to the world. This particular sadhana, called “The Vital Essence Sadhana of Dudjom T'hak-T'hung Pema,” was H.H. Dudjom Rinpoche's heart essence; by doing this practice, Dudjom Rinpoche overcame many obstacles and gained long life.
Ven. Bhakha Rinpoche with H.H. Dudjom Yangsi (Nepal, 2011)
I should add that since 2000 or 2001, Bhakha Rinpoche's sanghas in California had done a weekend Vajrakilaya intensive prior to Losar every year, up until last year. Last year, Rinpoche instead led a Dorje Drollo intensive before losar. Take from that what you will. The previous Fall as well, Rinpoche led a Dorje Drollo retreat at the Zuni Mtn. Stupa which was so well attended they didn't have room to fit everyone inside the stupa and it was apparently quite a show. I haven't had the fortune of practicing D.D. or attending any D.D. puja anywhere so I have no first hand comments of the practice. Rinpoche is on the recovery from a stroke last winter (please pray for his long life and excellent health) so it is tentative, but he is supposed to be leading another D.D. weekend at the Zuni Mtn. Stupa this September. If you're interested, visit http://www.zunimountainstupa.org
Bhakha Rinpoche has been stressing Dorje Drollo practice more and more in recent years, and there must be a reason...
Last thing I'll say, regarding Duru Dragpo vs. Guru DragPhur vs. Duru Dorje Drollo, they are certainly related in terms of all being wrathful G.R. Some termas have Drollo, some have Dragpo, some have DragPhur (or Guru Gragpo PhurJuk (Kilaya-Tail or Lower-Body Kilaya). In the Longchen Nyingthig cycle, the only wrathful G.R. practice is Lama Dragpo Ta-Kyhung Barwa, which is a combined manifestation of Guru Dragpo, Hayagriva and Garuda. Very powerful practice for overcoming obstacles, specifically disease and spirit harm from nagas. Relatively speaking, while Guru Dragpo and Dorje Drollo are distinct forms, in the actual words of the Takhyung Barwa sadhana Guru Dragpo is referred to as Dorje Drowo Lod (Drollod)...so hmmm.... (BTW if I am in dangerous waters regarding discussing these things, please tell me. I don't want to do anything wrong.) Similar practices exist in which Guru Dragpo (the Guru Rinpoche aspect) is replaced with Vajrapani. This is called Ta-Chag-Khyung-Sum (Tamdrin=Hayagriva, Chagna-Dorje=Vajrapani, Khyung=Garuda) in the Dudjom Tersar tradition and I think there is a Gelugpa version, too. So...each have their own unique story, appearance, origin and power, and in many ways are similar but are in fact distinct in certain ways, too. I guess karma determines our connection to one variant or another????
BTW I'm really not trying to show off here even though it seems like it. I happen to find all this stuff incredibly fascinating, and love these types of discussions. Simultaneously impresses and irritates the heck out of my wife, which is why I do this stuff at 1:30 am!