....I'm sure someone more local than I will explain the additional routes available on the Any Permitted ticket.
As far as routes go, in practice there will be no difference.
The 'Rte Metrolink CTLZ' ticket is valid on the tram in Manchester city centre, the 'Rte Any Permitted' fare is not. It could be argued that the 'Rte Metrolink CTLZ' is only valid when part of the route includes the tram. This comes about because 'Rte Metrolink CTLZ' should only exist where the journey 'requires' the use of Metrolink to get across the city centre, hence journeys like Bolton to Stalybridge do not have a 'Rte Metrolink CTLZ' fare, whilst journeys like Stockport to Ashton-under-Lyne do.
Looking at those links the thing that jumps out at me is that the £4.20 ticket has the new evening peak restrictions on weekdays whereas the £6.30 one doesn't.
It doesn't surprise me, though also of note is that, officially, the 'Rte Any Permitted fare is set by Northern whilst the 'Rte Metrolink CTLZ' fare is set by TfGM.