Although some believe the word tact is short for tactics in phrases like "change tact" or "try a different tact," the correct word in such contexts is tack.
Tack in "change tack" and "try a different tack" means "a course or method of action especially when sharply divergent from that previously followed.”
Tack developed this meaning from its nautical applications. In sailing, tack can refer to the direction that a ship or boat is sailing in as it moves at an angle to the direction of the wind; or to a change from one direction to another direction; or to the distance traveled while sailing in a particular direction.
Tack developed the "course or method of action" meaning near the end of the 17th century; within 100 or so years, the phrase "change tack" was being used with the figurative meaning it has today.
While there is also a long history of people using tact where tack belongs, the use is widely shunned by usage guides, which means you might want to avoid it.