Heidegger wants to avoid the speculation of previous science and philosophy. Although it is not a Heidegger word, I use ’speculation’ here with all of its connotations, pondering at a distance, but without commitment, or like spectators at a sports stadium looking in at something distant and other. In contrast, ready-to-hand suggests commitment, being actively ‘in the world’ and even when Heidegger talks about those moments when an entity ceases to be ready-to-hand and is seen as present-to-hand, he uses the term circumspection — a casting of the eye around, so that the Dasein, the person, is in the centre.
So present-at-hand is simply the mode of being of the entities that are not Dasein (aware of their own existence), but our primary mode of experience of them and thus in a sense the essence of their real existence is when they are ready-to-hand. I note Roderick Munday’s useful “Glossary of Terms in Being and Time” highlights just this broader sense of present-at-hand.
Maybe the confusion arises because Heidegger’s concern is phenomenological and so when an artefact is ready-to-hand and its presence-to-hand ‘withdraws’, in a sense it is no longer present-to-hand as this is no longer a phenomenon; and yet he also seems to hold a foot in realism and so in another sense it is still present-to-hand.