We use dream as a verb and a noun to refer both to hopes or grand plans and to the experience during sleep.
In normal conversational English, there is no more specific word to refer to the sleep experience, but there are many words that refer to hopes: aspirations, longings, objectives, passions, etc.
Context as well as syntactic cues normally make it abundantly clear which of the two the speaker is referring to, although there is some possibility for confusion.
Let's try one out.
I have a dream to travel the world.
I had a dream to travel the world.
No native speaker is going to think you are referring to the sleep experience. Notice that in the aspiration,there is an infinitival complement, to travel the world. An infinitival complement to dream is not normally used in contemporary English when dream refers to the sleep experience.
To refer to a recurrent sleep experience, a native speaker would say something like:
I keep having this dream where I am traveling the world.
If it were a single dream:
I had a dream where I was traveling the world.
I had a dream in which I was traveling the world.
In the sleep experience, when the dream is recurrent, the tense would be continuous (I keep having) which we would not use with an aspiration, and there is an adjunct clause that starts with where or in which, neither of which would we be likely to use in combination with a continuous tense to refer to an aspiration.
Now, the following could be ambiguous:
I have this dream where I travel the world.
It refers either to a recurrent sleep experience, or to a persistent wish or recurring reverie that seems to the speaker to have only a very remote chance of ever becoming a reality.