My understanding is this: angular momentum of a body about a point cannot be in two directions at once, which is why a wheel already rotating about its axle, cannot also rotate about its diameter at the same time; it tilts sideways. However this doesn't seem to be the case for points of reference outside the body?
For example, consider the earth, with a circular orbit around the sun for simplicity. Taking the sun as origin, the earth's angular momentum points perpendicular to its plane of revolution. However, the earth also rotates around itself, with the axis making some angle with the plane of rotation, so it has another angular momentum, pointing in that direction.
Can somebody explain how the second situation differs from the first?