The only "closeness" or resemblance between the two cartridges would be the use of 240gr bullets.
The mag can not perform optimal with slower burning rifle powders much slower, if at all, than the 2400/IMR4227 area burning powders...the 44-40 can at least perform. A reason is the weight of the bullets designed to be used by each. 200 vs 240.
The 44 Magnum is listed under both rifle and revolver in the SAAMI specs. while the 44-40 is only listed under the rifle specs.
The 44 magnum is listed as 1,700fps in a rifle (1,170fps/15" vented to 1,600fps/15" non-vented for pistols) with a 240gr bullet. The best I can get out of a 240gr bullet with the 44-40 is 1,500fps from a 20" MGM barrel I use for testing.....and with Ed's 43-230G bullet loaded with Reloder 7.....and that is pushing the 44 W.H.V. max pressures of only 18,000psi as compared to the 44 Magnum's 36,000psi range.
Thus there really is no "closeness" of the two cartridges.
Here is some work that Larry Gibson did a while back.
Phase two test results:
Six loads were selected to be loaded in both 44-40 and 44 Magnum cases for chronographing via the Oehler M35P using the Ruger OM Vaquero 7 ½” barrel revolver with both its original 44-40 cylinder and with the FTBH 44 magnum cylinder. I’ll also list the velocities chronographed with selected loads in the 44-40 Chiappa M92 carbine with 20” barrel.
Load………………………44-40 fps…44 Mag fps…M92 fps
429-200-RF/6.0 gr BE……..947……… 1016………..1188
43-206H/6.0 gr BE………...903…………970………..1121
43-230G/6.0 gr BE………...881…………937
TL430-240-SWC/6.0 gr 700X..858……...937………..1061
429-200-RF/25 gr RL7……1053………..1130…… ..1428
43-230G/25 gr RL7………..1071……….1163
TL430-240-SWC/25 gr RL7..1157…........1204……….1488
All loads in 44-40 cases gave less fps than the same load in 44 magnum cases in the same revolver. The average difference is the 44-40 produced, on average, 93.4% as much velocity in the 44-40 cases as the same load did in the 44 Magnum cases. That does seem to suggest that what I had read years back about the 44-40 producing 95% +/- as much psi as with the same load in a 44 Magnum case is correct. So, is there a correlation we can use to determine safe pressure 44-40 loads with pressure testing being done in the 44 Magnum pressure test barrel? It appears so. Since all was equal in the revolver except the chambering and since velocity is directly related to pressure [all other equal as was in this test] I think we can safely conclude a load that produces so much pressure in the 44 Magnum will only produce 93 – 95% of that pressure in the 44-40 cartridge.