How can gravity keep moons orbiting planets but also cause things to fall and how the interaction of inertia and gravity keeps Earth in orbit around the sun?
Newton's force of gravitation has a negative sign, which is why all these bodies fall toward the nearest attractor. The Moon falls onto the Earth, the Earth falls on the Sun, etc. It is also correct to say that all falling bodies move along their orbits. The difference is only if this orbit intersects with the finite dimensions of the attractor. Celestial orbits do not intersect with the attractor (usually), because they have sufficient kinetic angular momentum to stay at a distance. In other words, they move too fast (by inertia) in the tangential direction, so they miss the attracting body.