There are over 1000 operational satellites, and probably as many again defunct or non-operational satellites in orbit, plus a great deal more small pieces of space junk.
About half of these are in a low earth orbit (LEO). Satellites in LEO have a period of between 90 minutes and 130 minutes. But you would not expect a satellite to follow the same path in the sky in two orbits, as the earth will have moved between orbits of the satellite. So it is very unlikely that you will see the same satellite pass in front of the moon twice.
Satellites in LEO are moving fast! They will cross the moon's disc in less than a second, and transits are rare, as each is a path only 7km wide. at any one time, a transit is visible from less than 100th of 1% of the Earth's surface. To obtain the awesome photo that you have linked, the astrophotographer would have had to use some orbital prediction software to calculate the exact time of a solar transit by the ISS and travel to a carefully calculated position (and prayed for clear skies). You could be observing the moon all year and never see a transit.
Most of the remaining satellites are in Geostationary orbits, They orbit at a great distance over the equator. As their orbital period is exactly one day, they appear to hang in space above a point on the Earth. Such satellites are too distant to be seen as "dots".