Top Line, No. 1: If you saw a meteor and then you found a rock, the rock is not a meteorite.
Top Line, No. 2: If you found a rock, it might be a meteorite, but it is definitely not a meteor.
Meteor over Park City, Utah, August, 2016. Source: NASA/Bill Dunford
You cannot hold a meteor in your hand. A meteor (“shooting star”) is the visible streak of light in the sky from a meteoroid or micrometeoroid passing through the upper atmosphere of the Earth. The meteoroid compresses the air which causes the exterior of the meteoroid to heat and glow (incandesce). The meteoroid sheds glowing material in its wake, causing the streak in the sky. There is a meteorite there, but you cannot see it.
Meteoroids enter Earth’s atmosphere at speeds typically of 12-40 km/s relative to the Earth. That’s equivalent to New York to Los Angeles in 1.6 to 5.5 minutes.
A portion of the Self-Test Check-List. If you saw a meteor and you found a rock, the rock is not a meteorite.
Meteors stop incandescing (the light goes out) tens of kilometers above the Earth’s surface. It takes a few minutes for any surviving fragments to fall to the ground during the “dark flight.” They keep moving in same same general direction, but their fall becomes more vertical and is subject to wind speed and direction. The fragments land at terminal velocity, about 100-200 m/s. Meteorites are not glowing when they hit the ground and they are not hot. Also, meteorites are much smaller than most people think they are, typically a few centimeters in size. This all means that the meteorite fragments land far from where you last saw the meteor and there is no way that observers at a single point on the Earth’s surface are going to find fragments of the meteorite.
For another opinion, see also this.
Bottom Line, No. 1: If you saw a meteor and then you found a rock, the rock is not a meteorite.
Bottom Line, No. 2: If you found a rock, it might be a meteorite, but it is definitely not a meteor.