"May I receive the going forth under the Blessed One, may I receive the higher ordination?"
BB: The going forth (pabbajja) is the initial ordination as a novice (samanera); the higher ordination (upasampada) admits the novice to full membership in the Sangha as a bhikkhu.
"Kassapa, one formerly belonging to another sect who desires the going forth..."
BB: For details on the ordination of a wander formerly belonging to another sect, see Vin I 69-71.
Spk: The candidate is actually given the going forth and lives as a novice during the probationary period, after which the bhikkhus give him the higher ordination if they are satisfied with him. The Buddha, however, is entitled to waive the usual procedure when he recognizes that the candidate is sufficiently competent and need not be tested. In Kasspa's case he had the going forth given to him; then, immediately after, Kassapa was brought back to him and he called an assembly of bhikkhus and administered the higher ordination.