:???: Really? Even on journeys that don't go anywhere near the Manchester Central Zone? For example: Stockport to/from Hazel Grove, or Urmston to/from Flixton.
Stockport-Hazel Grove, or Urmston-Flixton definitely not valid on Metrolink city zone unless it's a season ticket, when it's valid for rail travel at weekends/bank holidays ANYWHERE in GMPTE area including Metrolink City Zone
Manchester Stations are Piccadilly, Victoria, Oxford Rd or Deansgate.
If the destination on your ticket is Manchester Stations it is not valid on Metrolink. Manchester Stations are Piccadilly, Victoria, Oxford Rd or Deansgate. (this ticket will have been bought outside Greater Manchester)
If the destination on your ticket says Manchester Ctlz (Central Zone) it is valid on Metrolink in the city zone to continue your journey from either Deansgate, Oxford Road, Piccadilly or Victoria. (it will be a single, return or season ticket from a Greater Manchester station (or Disley, New Mills Ntwn/Ctl, Knutsford, Ashley or Mobberley) to a 'Manchester Station'.
If the destination on your ticket is Metrolink City it is either
i)a ticket from stations between Hale on Mouldsworth allowing travel via Sale to any station in the Metrolink City Zone
or ii) a ticket from a station outside the GMPTE area with an add on to a city zone station eg. Blackburn - Market St, similar to a London Zone 1 add on to a London Terminals ticket.
If your ticket says Route Metrolink, you may use the Metrolink (for a cross city journey) You do not have to use Metrolink, and may travel via Salford Crescent (e.g Stockport - Rochdale) or Stalybridge (e.g Stockport - Greenfield).
The confusion arises because any permitted tickets are still in the system and allowed cross city travel eg. Stockport - Bolton via Stalybridge (before Metrolink and the Windsor link (Deansgate-Salford Crescent was built), and when there were frequent trains between Stockport and Stalybridge), these tickets were more expensive but meant passengers didn't have to get a bus between Piccadilly and Victoria. They remain in the system as 'any permitted' but are really obsolete and have no relevance today (and off peak a GM Rail Ranger is cheaper).