Someone who needs reading glasses to see at a close distance has problems her lens. someone who needs glasses to see objects at a distance has problems his lens.

Someone who needs reading glasses to see at a close distance has problems converging her lens. Someone who needs glasses to see objects at a distance has problems diverging his lens.

People who experience hyperopia  far-farsightedness) or presbyopia cannot see objects close by clearly without reading glasses. This is because their lens can no longer converge. In other words, their lens is unable to form a convex and significantly curved shape that is need to see nearby objects clearly.

People who experience myopia (or nearsightedness) cannot see objects at a distance without corrective glasses. This is because they have problems diverging their lens. Their lens is unable focus light rays back on their retina despite flattening of the lens to full capacity. Due to this people with myopia need glasses with concave or diverging lenses.