Sramana in that context obviously means a person who is in the habit of performing srama. Far from separating these seers from the vedic ritual tradition, therefore, śramaṇa places them right at the center of that tradition. Those who see them [Sramana seers] as non-Brahmanical, anti-Brahmanical, or even non-Aryan precursors of later sectarian ascetics are drawing conclusions that far outstrip the available evidence.
Theories on who influenced whom, in ancient India, remains a matter of scholarly debate, and it is likely that the different philosophies contributed to each other's development. Doniger summarizes the historic interaction between scholars of Vedic Hinduism and Sramanic Buddhism:
There was such constant interaction between Vedism and Buddhism in the early period that it is fruitless to attempt to sort out the earlier source of many doctrines, they lived in one another's pockets, like Picasso and Braque (who, in later years, were unable to say which of them had painted certain paintings from their earlier, shared period).
Various possible references to "śramaṇas", with the name more or less distorted, have appeared in ancient Western literature.
Clement of Alexandria makes several mentions of the śramaṇas, both in the context of the Bactrians and the Indians: