Mistrial is when the case has been hopelessly derailed, or "rendered invalid through an error in the proceedings," although it also encompasses deliberate misconduct. Dismissal is the result, but can be with or without prejudice. The default is without prejudice, and the case can be brought again, but with prejudice amounts in effect to an acquittal as the case cannot be tried again.
If the prosecution merely absolutely fails to prove their case, that's a different thing called a judgment notwithstanding the verdict. The defense can file a motion for this (or the court can rule it sua sponte) at the end of the prosecution's case, and if they have done so, again after the verdict. This is a different result and is not a dismissal, but outright counts as an acquittal.