A śramaṇa is, by necessity, a novice ordained by a bhikṣu. One does not require a quorum to ordain novices. I suspect that what happened in China was that many Central Asia and Indian monks came to China and ordained novices (śramaṇas).
Your use of the term śramaṇa is not universal. The term śramaṇa was used to refer to renunciates in general in several Āgama sūtras in classical Chinese translation I've read. Moreover, some monks, at least in China, self-identified as śramaṇa (Chn. shamen
沙門), but that wasn't because they were novices.
I mean just look at the definition of the term in the DDB:
# Transliteration of the Sanskrit, meaning 'a Buddhist monk' (or nun). A wanderer (Pāli samaṇa; Tib. dge sbyong). A world-renunciant religious practitioner striving for liberation. Originally in India, śramaṇa was a general term for a person who had shaved his head, renounced his worldly status and possessions and who trained his mind and body in the attempt to stop evil activities and strive for the good. It originally referred to non-Buddhist practitioners such as the Jains, who based their beliefs on the Vedas and Upanishads. Translated into Chinese with such terms as 息, 息心, 靜志, 淨志, 乏道, 貧道, 動息, 功勞, 勤息, 淨志, 貧道 etc. Also transliterated as 桑門; 娑門; 喪門; 沙門那; 舍羅磨拏; 沙迦懣曩; 室摩那拏, 舍囉摩拏. 〔長阿含經、 T 1.107a〕 (Skt. śrāmaṇaka, śrāmaṇya, śrāmaṇera, pravrajita) [cmuller; source(s): Hirakawa, JEBD, Yokoi, Soothill, YBh-Ind]
# (1) Ascetics of all kinds; "the Sarmanai, or Samanaioi, or Germanai of the Greeks, perhaps identical also with the Tungusian Saman or Shaman." (Eitel) (2) Buddhist monks "who 'have left their families and quitted the afflictions,' the Semnoi of the Greeks." (Eitel) "He must keep well the Truth, guard well every uprising (of desire), be uncontaminated by outward attractions, be merciful to all and impure to none, be not elated to joy nor harrowed by distress, and able to bear whatever may come." The Sanskrit root is śram, to make effort; exert oneself, do austerities. [cmuller; source(s): Soothill]
I don't think you can really argue for a huge difference between Central Asian Buddhism (define were, first of all) and Indian Buddhism because of the strong Influence of Indian culture from Bactria all the way to Java and Modern Day Vietnam.
Khotan and Kuci (Kucha) were the main cities.
How much do we know about the state fo monastic ordination in China prior to the 7th century?
I think we know a lot, though in English the resources for such research are slim. I read a thick book on this subject in Japanese.
In any case from the fifth century China had translations of four major vinaya systems, so everyone knew what a proper bhikṣu was.
In order to be a śramaṇa or a bhiḳsu, one needs to ordain in one of the "eighteen" schools. Otherwise, you are an upāsikā.
Apart from these categories there are no other categories of Buddhist practitioners, Mahāyāna or otherwise.
Right, but this was not the majority view of things in East Asia. Again this comes down to what a seng
僧 is. He is not be necessity a bhikṣu (though in many cases he would be), though he is still able to receive offerings from the white robed laity (upāsikā), reside in a temple, wear the kaṣāya and be addressed with a formal title.
At least in the Tang Dynasty I get the sense the vinaya was seen as just one set of disciplinary precepts that could make a seng
僧 as there were other viable options which were generally held as acceptable. Actually what really made a seng
僧 in that period was formal state certification of the fact, which in many decades could be easily purchased thus allowing anyone, monk or not, to avoid taxation and mandatory labour duties.
However, I know by the Song Dynasty they insisted all seng
僧 had certification of their vinaya ordination, which proved to be a problem for Dogen when he went to China.
Basically in Saichō's time in China the legal terminology determining what constituted a "monk" or seng
僧 was not based on Sanskrit definitions provided in the vinaya. I understand from an Indian or Tibetan perspective this appears odd, but that's just how it developed.