Strange to say, dogs have dreams

[keannu]

This means "Dogs dream while sleeping", but how do you say they have ambitions in the future, which may not make sense, but just to differentiate the two?

ex)Strange to say, dogs have dreams.

[Barb_D]

I guess you say they have aspirations or ambitions.

[JMurray]

This means "Dogs dream while sleeping", but how do you say they have ambitions in the future, which may not make sense, but just to differentiate the two?
ex)Strange to say, dogs have dreams.

To state that dogs are capable of dreaming while asleep I might say: "Dogs (do/can) dream", "dogs have dreams" or "dogs do/can have dreams".
But any of these is also ambiguous in the way you have indicated, in that they can mean that dogs have aspirations or ambitions of some sort.
A common way to make the distinction is by saying: "dogs (can) have their dreams (too)".
The ambiguity seems to still be there but I feel that most native speakers would take that to mean: "dogs have aspirations just as humans do".

not a teacher