The Hua Yen comes from Flower Garland Sutra - wikipedia says " The Huayan or Flower Garland school of Buddhism (traditional Chinese: 華嚴; ; pinyin: Huáyán, from Sanskrit: Avataṃsaka) is a tradition of Mahayana Buddhist philosophy that first flourished in China during the Tang dynasty. The Huayen worldview is based primarily on the Avatamsaka Sutra (Chinese: 華嚴經; pinyin: Huáyán jīng). The name Flower Garland is meant to suggest the crowning glory of a Buddha's profound understanding of ultimate reality.
The Huayan School is known as Hwaeom in Korea and Kegon in Japan. This tradition also had a strong influence on Chan Buddhism."
This teaching is the basis of Thich Nhat Hanh's terminology substituting "Interbeing" for Sunyata (Emptiness) - because sunyata isn't simply an "essential nature" of everything. Viet Chan/Zen is very strong in this teaching.
Full text of Flower Garland Sutra:
Tiantai, on the other hand is based on the Lotus Sutra. Again the Wikipedia summary is sufficient: https://en.wikipedia.org/wiki/Tiantai
"Tiantai (Chinese: 天台; pinyin: PRC Standard Mandarin: Tiāntāi, ROC Standard Mandarin: Tiāntái) is a school of Buddhism in China, Japan, Korea, and Vietnam that reveres the Lotus Sutra as the highest teaching in Buddhism. In Japan the school is known as Tendai, in Korea as Cheontae, and in Vietnam as Thiên thai.
The name is derived from the fact that Zhiyi (538–597 CE), the fourth patriarch, lived on Tiantai Mountain. Zhiyi is also regarded as the first major figure to make a significant break from the Indian tradition, to form an indigenous Chinese system. Tiantai is sometimes also called "The Lotus School", after the central role of the Lotus Sutra in its teachings.
During the Sui dynasty, the Tiantai school became one of the leading schools of Chinese Buddhism, with numerous large temples supported by emperors and wealthy patrons. The school's influence waned and was revived again through the Tang dynasty and also rose again during the Song dynasty. Its doctrine and practices had an influence on Chinese Chan and Pure land Buddhism."
Also very big influence on Chan/Zen, as in these traditions an idea of Pure Land teaching is probably encouraged, particularly among the laity. Tiantai is credited with being the first truly Buddhism of Chinese origin.
Full Text Lotus Sutra: http://www.bdk.or.jp/document/dgtl-dl/dBET_T0262_LotusSutra_2007.pdf