Freud says the original dream content is usually obscure, incoherent and highly symbolic, so our memory of it is fragmented, at best.
On waking, the conscious mind fills in the gaps to make sense out of the dream, even though our waking interpretation doesn’t necessarily fit with the actual dream content.
Encyclopedia Britannica says:
The final function of the dreamwork is secondary revision, which provides some order and intelligibility to the dream by supplementing its content with narrative coherence.²
In his Dictionary of Psychology, J. P. Chaplin calls this secondary elaboration, and says we essentially try to make a better “story” out of the dream content.³
¹ The Interpretation of Dreams (German edition: 1899 & 1900).
³ Dictionary of Psychology (Bantam: 1985).