As @deutschZuid said, there is no such thing as an upgrade from physical to digital copy, which means you'll have to pay full price again, unless you somehow got a lucky deal on a digital copy.
However, if you ever do choose to purchase the digital copy, your savegames will keep working. That is assuming both physical and digital copies were from the same region. If you bought an imported physical copy, then at a later time a regional digital copy, the saves might work, but they also might not. There is no guarantee they will. The same is true for any DLC you might've purchased; they will work on both the physical and the digital copy, assuming both were from the same region.*
*: The statement about savegames and DLCs is true for PS4 (and PS Vita). I haven't verified it on Xbox One yet, but I suppose it should be true there as well, at the very least for DLCs.