new trial:

1. A re-examination of an issue of fact by the trial court with a view to correcting errors which have occurred in the course of the former trial.  State v Burns, 312 M0 673, 280 SW 1026, 44 ALR 848.

2. A re-examination in the same court of an issue of fact after a verdict by a jury, a report of a referee or master, or a decision by the court.  39 Am J lst New Tr § 2.

3. A remedy sought by motion made in the same action.  39 Am J 1st New Tr § 186.

new trial on appeal:

1. A new trial or trial de novo with limitations.
     The normal review on appeal or by error proceeding is confined to consideration of the record below, with no new testimony taken or issues raised in the appellate court, the tendency being to limit appellate courts of final jurisdiction in their consideration of questions of facts. 4 Am J2d A & E § 1.

2. The nearest approach to a complete trial de novo on appeal is in an appeal or error proceeding taken from a decree in equity, where the appellate court can make independent findings of fact, drawing its own conclusions from the evidence, but even in this instance the review is limited to a consideration of the record made in the lower court.  5 Am J2d A & E § 703.

rehearing on appeal:

1. See rehearing; trial de novo.

trial de nova:
(tri’al dé nō’vō)

1. A new trial; a new trial on appeal. 4 Am 12d A & E §2. 

2. A trial on appeal from a justice of the peace to a court of general jurisdiction.  3I Am J Rev ed J P §129.

3. Trying anew the matter involved in an administrative determination the same as if it had not been heard before and as if no decision had been previously rendered, the hearing being upon the record made before the administrative agency and such further evidence as either party may see fit to produce. 2 Am 12d Admin L §698. [2]