GTR is a TOC; the constituent route brands are not TOCs and have not been for years.The REOs will span all GTR TOCs, but they're employed by their former TOC (Southern or Southeastern for example), so there's quite a few about now I guess? And as such will patrol their individual TOC area (so Southern would go as far as Brighton, whereas SET obviously wouldn't?). Unlike like the RCOs who at present only work on the SWR network and not across all FirstGroup TOCs (there's only 30 for the whole network give or take).
At times, GTR does act in a way that is designed to mislead people into thinking each of their route brands is a separate TOC (for reasons I won't go into now!), but they do admit the truth in their Passengers Charter.
Govia Thameslink Railway is the name of the company running your train service. There are four routes: Gatwick Express, Great Northern, Southern and Thameslink. This is the largest franchise in the UK, with 22% of the UK’s passenger rail services.