Help identifying/making gear for my DSG lathe

I'm just a little baffled that one gear is almost 10mm bigger than the other and they are supposed to be (I think) the same gear profile.
The OD size of the gears depends on the DP/module and the tooth count. If the larger gear is also 48 teeth, then it can’t be the same DP as the smaller gear.

For that gear train, all the gears must be the same DP/module to operate properly, but that doesn’t mean someone didn’t put the incorrect gear in there somewhere in the past. Or it could have come off a different lathe and got mixed up with that lathe at a previous owner. I would suggest measuring all the other gears in that train to determine the DP and see if it is consistent, and if so, then you know what DP you need to get.
 
To cut the correct tooth profile for different tooth count gears it takes a different cutter. It takes 8 cutters to make a set. #1 thru 8.

Gear cutters, Spur gears
Module 1.25
20° pressure angle

# # of Teeth
1 12 – 13
2 14 – 16
3 17 – 20
4 21 – 25
5 26 – 34
6 35 – 54
7 55 – 134
8 135 - ∞

Diameter of gear, N+2/DP , DP=25.4/Module, # teeth+2/20.3 = “ [for Module 1.25 (my lathe)]
Circular pitch CP-PD* pi/N or pi/ DP or OD*pi/N+2 or 2*T
Diametral Pitch DP=N/PD or N+2/OD or pi/CP or 25.4/M or pi/2*T
Module M=PDM/N or 25.4/DP
Pitch Diameter PD=N/DP or N*CP/pi or OD*N/N+2
Outside Diameter OD=N+2/DP or CP(N+2)/pi or for my M1.25 lathe gears N+2/20.3
Thickness of tooth along the curve @ pitch circle T=CP/2 or pi/2*DP
Chordal Thickness Measured along the cord @ pitch circle (straight line) CT=PD*Sin(90/N)
f clearance at bottom of the tooth f=T/10
D+f=2.157/DP or .6888*CP
For a Module 1.25 gear OD=N+2/(25.4/M) My lathe change gears.
 
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