Child or Minon?

To make a vampire they have to suck your blood. And then you have to
suck their blood. It's like a whole big sucking thing." -- Buffy

The Master sired Darla. 
Darla sired Angelus. 
Angelus sired Drusilla.
Drusilla sired William The Bloody/Spike.
They all belonged to The Order of Aurelius. 

Each was of these vampires were considered to be a child of their sire.
My question is why does one become a child and not a minon?
Is there a special ritual for one to become a child and not just a minon?
Was it ever addressed in canon?