Subjectively, phenomenologically, dreaming mostly seems like another world.
To drop-into a dream is to drop into an on-going' narrative - something which was already-going before I began to dream it, and which continues after I waken.
Also, dreams usually feel like another time, another place, and without connection with my waking life except for it being 'me'.
(A few dreams are connected with waking life, but these are rarer and seem to be shorter and less complex - the kind of dreams I get when frequently dozing and waking.)
In commonsense terms, dreams feel like the mind goes somewhere else - moves in space and time, in dreams I am both a time traveler and a place traveler; in other words that experiences of 'shamans' are the normal experiences of dreams.
(This sounds much more exciting than it really is. My major experience of dreams is boredom and futility - just b&f in other times and places.)