Mapsource has been superceded by Basecamp, but there are many here who still prefer to hang on to Mapsource. As I was new to both, I decided to stick with Basecamp.
Basecamp is a free download from Garmin (I believe). That said, there was a disk in the box when I got my Nav IV. It was not specifically labelled as 'Basecamp", but when I ran it, that is what it loaded onto my laptop.
Anyway, make sure that you register your new Nav IV online (sorry, I may be teaching you to suck eggs, but having your device(s) registered online makes life a lot easier down the line.
If you create a map in Mapsource/Basecamp it is preferable to make sure that you use the latest map updates and that they are on both mapsource/Basecamp and your Nav IV.
If you have downloaded the lastest update (2014.10) to your Nav IV, then that is what it is using as, by default (I believe) it deletes older versions of maps.
That is NOT the case with Basecamp (and, I assume, Mapsource). The software retains the older versions. So you need to specifically select the latest version of the maps. In Basecamp I select the "Maps" dropdown menu and select the latest version (City Navigator Europe NT 2014.1)
From what you write, it sounds like you have different versions of the maps in mapsource and the Nav IV. Or that you may have the latest version of the maps on your Nav IV, but that you had not selected them as your default maps before making the route.
If it were me, in Mapsource, I would select the latest version of the maps; then open the route; and then recalculate the route. I doubt if anything will change, but just give the route a check and see that there are no funnies.
Then, having done that, transfer to the Nav IV.
Alternatively, just say yes when the Nav IV says it wants to recalculate the route and then check it on the screen when it has done that. Personally, I think it is easier to do this on a computer screen, which is why I recommend my first option.
Others may have other views and I am sure they will chip in