Satellites can be in orbits of various altitudes from ~100 miles to >20,000 miles above the ground. The higher you go, the longer it takes to complete the orbit. The Space Station is at 190 miles altitude – takes 90 min to go around. Communication satellites are in a geosynchronous orbit at 22,300 miles altitude – takes 24 hr to go around. I’m not sure about spy sats.
It helps me visualize an orbit by thinking of Saturn’s rings. If the ring is parallel to the equator, the satellite always flies over the equator. Note that a spot on the ground at the equator goes around Earth’s axis in 24 hours. So if you are in a low orbit, you will go faster than the spot on the ground, and (relative to the ground) move in an easterly direction. That might be good for observing things along the equator.
If the ring is tilted relative to the equator, you will go from NW to SE on one side of the orbit, then SW to NE as you loop around back. Check for yourself using a ball and a ring-shaped object. This is called an inclined orbit. If the axis of this orbit rotates around Earth’s axis, the satellite goes over much of the Earth’s surface. In fact, if the orbit is inclined 90° to Earth’s axis, it covers ALL of the Earth’s surface. Most spy sats are in inclined orbits so that they can cover a lot of area. Since little population is in the polar regions, few spy sats are in 90° inclined orbits.
To shift coverage, one can cause more tilt to view higher latitudes. To change timing, one can cause the axis of the orbit to rotate more or less than it currently is. Bad guys often have a lead on satellite position, so can calculate when the next pass will be. They then hide their stuff until after the sat has gone by. If the axis were suddenly changed, the overfly event will not be as calculated and their attempts at hiding will be in vain. All this is accomplished through clever use of rocket thrusters.
Geosynchronous sats stay over only one patch of ground. To reposition, they use thrusters to go to slightly higher or lower orbits. When they do that, their speed will no longer be 24 hours to get around. They will move E or W relative to their original ground location. When they are above the correct patch of ground, they go back to 22,300 mile altitude and synchronize back to Earth’s rotation.