The map on the turn report is slightly different from the original galaxy game. This is to limit your knowledge of the galaxy to that which you have actually explored yourself and to account for asteriods.
Probably the biggest change is that the galaxy wraps. This means that all races start in equally dangerous positions. The positions of planets and ships are all displayed relative to your home world (this is to confirm your suspecions that the galaxy does revolve around you).
All objects within single jump range of your occupied worlds are displayed. There are two ways to expand your view of the galaxy. One is to settle new worlds. The other is to improve your drive tech. As your drive tech improves, so does the distance your drones can go in a single jump. Your map will display everything within that distance of your occupied worlds.
All ships in hyperspace, within viewing distance of your occupied worlds, will be displayed on the map. Groups of alien ships, with composite mass greater than one and whose destinations are one of your worlds, will also be listed in the incoming ships section of the report.
We have had to redefine some of the symbols on the map, this may be the most difficult change to get used to.
Asteriods are size zero worlds that may not be settled but may be used as a destination for ships in hyperspace.
One nice feature about the report is that once your have explored a world, the report continues to display the knowledge you have about that world. If it was uninhabited, then its size and resources will be displayed. If it was inhabited (and you successfully orbitted it), it will be listed as belonging to an alien race and the stats pertaining to that world will be listed along with the turn at which you last observed the world.