It can be just bollocky titles, but generally the DoF would manage / control the budgets, the whole football operation, etc.
What we’ve got is Tom Rawcliffe doing some of that (Football Operations and Football budgets) with some support from Gavin Marshall, whereas Tins is looking after the Recruitment Team, amongst other things.
If that makes sense.
Keith Burt was the last DoF, even then I think he didn’t have all the Operations stuff under him.