Does the slide from the 9mm sigma fit the 40 sigma frame? Does the slide from the 2gen sigma fit the first gen sigma?

I looked on Numerich Arms schematic and the slide for the SW40F has a different part number than the SW9F slide but they don't sell the frame so you can't check the part numbers.  By looking at the Schematic for the SW40F and SW9F the frames appear to be the same or similar like the Glock 23/19 frames are the same but the ejectors are different and the 9 & 40 have different part numbers for the ejectors.

You might join the S&W Forum and ask there but I don't have access to the second generation Sigma.  A Friend used to own a 9 & 40 Gen 1 Sigma and I think the frames were the same.  Seems like I remember him swapping slides between the 9 & 40 but that has been about 20 years ago.  You might call Brownell's techincal support or S&W CS they might give you the info.

https://www.gunpartscorp.com/Manufacturers/SmithWesson-33495/AutoPistols-42024/SigmaSeries-35314/SW40F-41956.htm