I don't think the Connect map (a particularly nasty example of bad graphic design) is intended to show all stations called at. It may be attempting to show the Connect stations that are going to be enhanced, but the exact calling pattern isn't known. I'd hazard a guess as non-stop Sheffield to Worksop because none of the stations in between seems very major and as mentioned there will be a replacement service for them. Then all of them would call at Retford and Gainsborough. .
As I quoted in post before yours the franchise TSRs, which define the number of calls at stations which the franchise are contractually obligated to provide are a far better source of information than any map.
On the Sheffield to Lincoln line, there is 1tph to all stations except Worksop and Retford which receive 2tph. The service is thus most likely an hourly stopper to Retford and an hourly Connect Service first stop Worksop, then all stations to Lincoln.
It's a bit more tricky where Connect is replacing rather than supplementing the existing stopping service so will have to provide local calls. The only two I can think of are the Nottingham (Dronfield, Langley Mill, Ilkeston - two of the three outside Rail North area so they probably aren't bothered)
The Nottingham-Sheffield Connect service will call at Ilkeston, Langley Mill, Alfreton, Chesterfield and Dronfield, the latter 2 stations getting an extra non-Connect service.
and the minor stops east of Carlisle (some perhaps only every two hours?).
As
Clagmonster says the Carlisle to Newcastle hourly Connect service will supplement an hourly slower service. The Connect service calls at Hexham, Prudhoe and Metrocentre only. The stopping service calls hourly at all stations except Wetheral, Brampton, Bardon Mill and Blaydon (only every two hours).
On Sheffield-Leeds I think the Connect will be flighted with the XC service to minimise capacity issues, ideally a few minutes before it in each direction so as also to remove local journeys from the XC as much as possible. For this to work it needs to have the minimum of stops and I'd guess just Meadowhall and Westgate.
The stopping pattern of this service is more difficult to work out from the TSR tables. A text note says it stops at Westgate and yes it may be one of the 8tph to stop at Meadowhall. It certainly doesn't stop at Rotherham or Swinton (which both receive only 1tph Leeds and 2tph Doncaster stoppers) or any other intermediate stations.
