They are both apparent realities experienced. The 'link' between the two states is the perceiver. The perciever experiences, is presented, with each state separately, the perceiver does not, cannot, experience both states at the same time. The perceiver is only aware of mental states. The Mandukya Upanishad IV says (The Upanishads: A New Translation by Swami Nikhilananda):
The second quarter (pada) is Taijasa, whose sphere of activity is the dream state, who is conscious of internal objects, who is endowed with seven limbs and nineteen mouths, and who is the experiencer of subtle objects.
And in his commentary on this verse, Nikhilananda writes:
INTERNAL: In dreams mental states consisting of the impressions of the waking state are experienced. During the dream state the sleeping man is aware of the external world and internal ideas. But when he awakes and reviews the dream experiences, he comes to realize that they were nothing but the internal activity of the mind. When a man is asleep his sense-organs are inactive. Therefore the dream experiences cannot but be mental states.
...SUBTLE OBJECTS: In the waking state one's consciousness is associated with gross objects, wheras in the dream state one sees the impressions of past experiences. But in reality the experiences of waking and dream are of the same nature; for in both states the perceiver is aware only of his mental states. [the link] From the standpoint of dreams, the dream objects are as gross and physical as those experienced in the waking state. It is from the standpoint of waking alone that one infers that the dream objects subtle, insomuch as in the dream state no gross object exists for the dreamer.
[and further in his adaption of Shankara's commentary] "Then [when he falls asleep] after having taken away with him [a portion of the] impressions from the world of the waking state, [destroying and building up again] he experiences dreams by his own light." Brhadaranyaka Upanishad IV. iii. 9.