No, they don't
What is shared are the magic item slots, not magic items.
Of course, a character may carry or possess as many items of the same type as he wishes. However, additional items beyond those in the slots listed above have no effect.
In other words, between you and your eidolon, you can only benefit from a single magic item per slot, be that an amulet, or a magic armor, or a shoulder magic item, and so on. Each slot can either benefit your character, or your eidolon, but not both of you at the same time.
Also, since you (or your eidolon) can only benefit from a single magic item, that means that you could even use two items on the same slot, but you will have to pick one of them to benefit either of you. This is exactly like wearing multiple rings, but only two taking effect at one time, which is the example used by the Link ability:
the summoner and his eidolon share magic item slots. For example, if the summoner is wearing a ring, his eidolon can wear no more than one ring. In case of a conflict, the items worn by the summoner remain active, and those used by the eidolon become dormant.
He says that the "eidolon can wear no more than one ring" because the summoner is already using one ring, and we know you only have two magic ring slots.