The orbit of an astronomical body around another astronomical body is an ellipse, with the primary in one of the two focal points of the ellipse. Thus the orbiting body gets closer to the primary until it reaches its closest point, and then gets farther away from the primary until it reaches its farthest point, and then gets closer again.
When an astronomical body orbits around another astronomical body, it will gain speed as it gets closer to its primary, but gaining speed will make it move farther from its primary, and as it moves farther from its primary it will lose speed, until losing speed causes it to move closer to the primary, in an eternal cycle.
According to Wikipedia, the Moon's perigee, its closest distance to Earth, is about 362,600 kilometers, but varies from 356,400 to 370,400 kilometers as the Moon's orbit slowly becomes more elliptical and then becomes less elliptical.
According to Wikipedia, the Moon's apogee, its farthest distance from Earth, is about 405,400 kilometers, but varies from 404,000 to 406,700 kilometers as the Moon's orbit slowly becomes more elliptical and then becomes less elliptical.
So that means that the apogee of the Moon is about 42,800 kilometers farther from Earth than the perigee of the Moon is. Because the Moon's orbit slowly becomes more or less elliptical, the difference between the apogee and perigee varies between 34,000 and 50,300 kilometers.
Meanwhile, the tidal interactions between the Earth and the Moon cause the Earth's rotation to slowly get slower, so that the length of an Earth day gets longer, and the Moon slowly moves farther from the Earth.
How slowly does the Moon gradually get farther from Earth?
Measurements from laser reflectors left during the Apollo missions (lunar ranging experiments) have found that the Moon's distance increases by 38 mm (1.5 in) per year (roughly the rate at which human fingernails grow).
Wikipedia: Moon#Tidal effects
So at that rate, it should take the Moon about 26,315.789 years for The Moon's average distance to get 1 kilometer farther from Earth, and about 42,240 years for the Moon's average distance from Earth to get 1 mile farther from Earth.
And in a single month the Moon's distance from Earth varies by about 42,800 kilometers or 26,594.687 miles.
So the very slow and gradual constant movement of the average distance between the Earth and Moon away from the Earth is real, but much smaller in scale than the monthly movement of the Moon toward the Earth and then away from the Earth during a single orbit around the Earth.