An entire complete shit. When a full one is taken, there is no need to return later because there is no shit left.
"I don't take half shits! That was a full one."
"Dude, watch the front desk. I gotta go take a full one."
An incomplete bowel movement. Taking a half shit implies that one will have to return later to complete the shit.
"Person X: Do you ever take a shit but know you'll have to do more later?
Person Y: Dude, I don't take half shits! Only full."
"I'm really constipated today, and I could only take a half shit."