Acting was a temporary advancement in rank or assignment, unlike a more permanent field commission.
Pavel Chekov served as the acting science officer aboard the USS Enterprise, following the death of Captain Spock. (Star Trek III: The Search for Spock)
Following the murder of Lieutenant Tasha Yar, Captain Picard made Lieutenant Worf the USS Enterprise-D's acting Chief of Security, until he was promoted to the position full time, when he transferred from the command division to the operations division in 2365. (TNG: "Skin Of Evil", "The Child")
After the Malcorian physician Berel had been relieved of his duties as Director at the Sikla Medical Facility in 2367, the position of acting director of the facility was passed on to Nilrem. (TNG: "First Contact")
In 2372, Vice Admiral Leyton promoted Captain Benjamin Sisko to acting head of Starfleet Security on Earth, due to his knowing more about the Dominion than anyone in Starfleet, during the Admiral's attempted coup d'état of the Federation. (DS9: "Homefront", "Paradise Lost")
On the USS Valiant in 2373, the seven regular officers were killed in a skirmish with a Cardassian battle cruiser leaving the Red Squad cadets to run the ship. Many were field promoted by Tim Watters to various ranks after he assumed command of the vessel. Watters, himself, was ordered by Captain Ramirez to take command of the vessel prior to his death. (DS9: "Valiant")
The fact that Dorian Collins was promoted to "acting" chief petty officer indicates that their promotions were intended to be temporary.
A short time later, Brunt took over the role of acting Grand Nagus after Zek had been deposed. The fact that he was merely the "Acting Grand Nagus" was repeated on several occasions, whenever anyone spoke of Brunt as "the Grand Nagus", alone. (DS9: "Profit and Lace")