Special Jonin was a rank between Chunin and Jonin, for those whose overall abilities did not meet all the standards of a full-fledged Jonin.
They were specialist ninja selected for possessing Jonin-level proficiency in a particular field.
In fantasy cultivation terms, this was half-step Jonin.
Peak Chunin!
They had Jonin-level proficiency in one area, but their overall strength fell far short of a Jonin's.
Baki was also a minor supporting character of some significance, in a Sand Village where the Fourth Kazekage had died and Chiyo and Ebizo had retired.
Baki could be considered a pillar holding up the Sand Village!
It was his firm support of Gaara that allowed Gaara to grow and gave the Sand Village a new pillar.
As an Elite Jonin of the Sand Village, he relaxed once he saw that the eavesdropper was a Special Jonin.
He did not believe that Hayate could escape with him and Kabuto blocking his way.
"Cough..."
Hayate coughed, staring grimly at Baki. "Baki, your Sunagakure has some nerve. You actually intend to attack the Leaf Village?"
Baki sneered. "Every man for himself, or heaven and earth will destroy him."
"This is all because your Leaf Village went too far. You stole the share of missions that should have belonged to us. Even people from our own country give their missions to your Leaf Village."
"You won't even leave us scraps, so don't blame us for being ruthless."
All conflicts were struggles over resources.
The Sand Village wanted to attack the Leaf Village for precisely that reason: to crush it, reclaim the share of missions that should have belonged to them, and take over the Leaf Village's missions along the way.
After the Third Shinobi World War ended, the Sand Village had been on the back foot at every turn.