"QUESTION: What's the difference between a writ and an appeal?
ANSWER: Writs usually are considered to be extraordinary remedies, meaning they are permitted only when the defendant has no other adequate remedy, such as an appeal. In other words, a defendant may take a writ to contest a point that the defendant is not entitled to appeal.
Any one of the following reasons, for example, may prohibit an appeal (and justify a writ):
(1) The defense did not lodge a timely objection at the time of the alleged injustice.
(2) The matter at issue concerns something that goes beyond the trial record.
(3) A final judgment has not yet been entered in the trial court, but the party seeking the writ needs relief at once to prevent an injustice or unnecessary expense.
(4) The matter is urgent. Writs are heard more quickly than appeals, so defendants who feel wronged by actions of a trial judge may need to take a writ to obtain an early review by a higher court.
(5) The defendant has already lodged an unsuccessful appeal (in some cases, defendants may file multiple writs, but the right to appeal is limited to one)." -From, "The Criminal Law Handbook" By: Bergman & Berman-Barrett