"Rest days" are not legal days off. A legal day off has to include two local nights so if you have a duty that finishes after midnight the remainder of that day becomes a rest day (you will be too knackered to do anything anyway). Similarly, if you have a duty that starts between midnight and 6am (lots of those by the way) then the previous day is a rest day.
Hope that makes sense. Almost all layovers are around 24 hours so there is very little opportunity for days off down route anyway, but the company doesn't count those days towards you legal minimum of 8 days off a month (yet!).
There is no minimum requirement for days off between trips at home unless they are ultra long haul or covered by an annexe to the FOM.