"To Mars" just means that the target of the mission is, in some meaningful sense, the planet Mars. It doesn't have to be a landing; an orbit around the planet or a close flyby also qualify.  However simply going out past Mars's orbital distance from the sun, while not actually approaching the planet itself, does not count.

"Send" means that the rocket actually started on its mission. A mission that is simply scheduled for the future does not count. A mission that lifts off and then blows up 2 feet above the launch pad still counts. The precise cutoff point will be main engine start.

If there's a mission that is half-jokingly described as aiming for Mars, but clearly had no hope whatsoever of actually getting there, that doesn't count. It must be a serious attempt. (But something as low as a 10% chance is still a serious attempt.)

"Starship" refers to the second stage only. A Superheavy first stage does not have to be going. If they rename Starship to something else, that still counts. (Please note that this is about sending the 

 Starship to Mars, not just using Starship to launch a smaller vehicle towards Mars and then turn back towards Earth.)