There are several Schools of Thought in Tibetan Buddhism but all recognize the Dalai Lama as their spiritual leader. He is like the Pope of Tibetan Buddhists in some ways

 The schools I was most associated with so far are Nyingma and Kagyu and Gelukpa.

Since Both the Dalai Lama and Geshe Lobsang Gyatso who we brought back to the U.S. after the Kalachakra Initiation in December of 1985. Geshe Lobsang Gyatso I think arrived here in the U.S. in California either March or April of 1986 and we arrived I think in April of 1986 back to the northern California coast near the Greater San Francisco Bay area. 

Both the Dalai Lama and Geshe Lobsang Gyatso are Gelukpa and the term Geshe means literally "Spiritual Friend" which Geshela definitely was for my family while he was still alive. 

Nyingma was directly from Padmasambhava and is the most ancient School of Thought

Next came Kagyu which came from Marpa the Translator through Milarepa.

Next, if I have this correctly came Gelukpa which is what the Dalai Lama is which is more intellectual sort of like College professors kind of lineage but also formed the government of Tibet around the Dalai Lama as the leader through 14 generations of Dalai Lama who are all considered to be reincarnations of the same Great Soul who is an incarnation of AValoketeshvara "The Buddha of Compassion".

There is also the Sakya school of thought which I know the least about at present but I'm learning new stuff all the time and often I put some of my research about what I'm learning here at my blog.

By God's Grace

Tashi Delek (Good Luck in Tibetan)