The pair were charged by the FA following a touchline incident in the fiery encounter between the two sides at the City Ground on April 1.
There was an added edge to the Premier League clash, after a melee between the two sides in the Carabao Cup quarter-final back in January.
It all boiled over again in the second half of the April Premier League clash - with both benches involved.
Sanz and Forest assistant boss Tate were sent off in the 52nd minute and subsequently charged with 'improper and/or violent conduct'.
Sanz admitted his behaviour was improper and Tate admitted a charge of improper and/or violent, and in a statement from the FA read: "Wolverhampton Wanderers' Pablo Sanz and Nottingham Forest's Alan Tate have been give one match touchline bans and £6,000 fines for misconduct.
"It was alleged that the assistant managers' behaviour during the 52nd minute of their Premier League game on Saturday April 1 was improper/and or violent."
Later in the feisty affair, which ended 1-1, Wolves' goalscorer Daniel Podence was alleged to have spat at Forest winger Brennan Johnson, and was subsequently charged by the FA.
However, an independent regulatory commission concluded it was 'not proven' that Podence spat at Johnson.