well we dont know what the Williams review will ultimately say but difference between centralisation and nationalisation is who runs the trains
with centralisation TOC's still exist and provide the drivers, staff etc but with government oversight on issues such as ticket price and timetabling, its a concession model like the Overground and Crossrail, rather than now where TOC sets prices then passes X% of profit to Gov, Gov set prices then pays TOC a fixed operational cost
with renationalisation gov would take over the actual day to day operations, e.g. driver and train staff would be government employees with there pay coming directly from DfT rather then via a TOC, in fact all private TOC's could cease to exist apart from open access operators