Lineage is important to Buddhists. It's the only way to be sure you are receiving Buddha dharma teachings that are genuine. Buddha Sakyamuni set forth the guidelines over 2,500 years ago in the Vinaya Pitaka one of the three baskets forming the Tripitaka. As soon as his students had disciples thus the varied schools were born and generations after joined, created, merged with others.
There are various schools that have different versions of the Vinaya Pitaka and some differences in compilations of sutras depending upon the means and skills of the scholar monastics of the time, funding by royalty and merchants to pursue sutra copying and eduation and this is normal for throughout the history of Buddhism.
There is only one unbroken active school in the Bhikshuni lineage surviving to this day. Presently there are 6 schools translations of the Pratimoksa in english with only 3 of the main ones being practiced as of 2010. There has been just one unbroken Bhikshuni line out of these schools, that of Dharmagupta/Dhammoguptaka. This is continued to the present day in Taiwan, China, Korea, and Vietnam. This school's direct line is from India to Sri Lanka then to China to Taiwan, Japan (destroyed in Meiji period), Korea, and Vietnam.
Restorations one lineage and the creation of another:
How it was perceived in the past. Bhikshunis were actively practicing in the immediate presence of the Buddha, schools varied normally by the teacher who gathered students around him or her and a group voted upon what constituted that school People came after to join and test out if they like to continue or left knowing they could not, normally that is the way it's done. Some schools merged and faded with time. That is normal. What makes a community is it's ability to live in harmony and the Vinaya guides us on that, Differences happened when teachers used wisdom to change something in the rules and the community accepted or rejected the change. Very rarely did conflicts require the country council to intervene unless there was significant property or financial disputes.
Who decides what rules or schools to follow? The immediate community that observes the Vinaya rules does. That means bhikshus and bhikshunis decide which groups they live in or don't; and communities may or may not restrict membership to their own little groups or major schools that they created and approved; what succeeds is what works in the present time, not the past, not the future but the NOW of this moment!
Theravada being active with Bhikkhu and newly establishment of the new Theravada Bhikkhuni Sangha from Sri Lanka, Australia, and Thailand (albeit presently illegal in Thai Sangha).
Mahayana has Tibetan Bhikshus with no Bhikshuni Sangha accepted or established until a recent comment by the Karmapa who said he would do it... their Maha Sangha has rejected repeated requests by elder's supporting the first Tibetan Bhikshuni Sangha there.
There are emerging schools as there as always been; terms 'therevada' and 'mahayana' are only conveniently assigned in the West by scholars as a conversation starter while as monastics we have a more universal viewpoint that depends on relationships, community access and personal practices.
Ven. Hong Yang is Chan Linji the 56th generation of the inner name Hong宏 and the 67th generation of the outer name Guang光. She has training in Pure Land from her tonsure temple and can offer the Pure Land practitioners around the world continued training. She has certified to teach meditation since 1990 by a Buddhist Shaolin master, later also certified by a Bhikshu in 1995.
Please be a part of the important preservation of our lineage in the present bhikshuni sangha and donate generously.