When shopping online for .38 spl. I came across some .38 short. Can you shoot .38 short from a gun chambered for .38 spl.? If so then I guess it would be safe to shoot from a .375 also.

The 38 Short is the parent to the 38 Spcl, et al.  So yes you can shoot a 38 Short in a 38 Spcl, 357, etc.  Because of the long bullet jump (distance to the forcing cone of the barrel) accuracy may suffer. Your chamber cylinder may also develop a powder ring making it hard to chamber or extract longer cartridges without a real good cleaning.  No one I know of shoots 38 shorts, they just load low power 38 Spcl.

If it's a 38 short COLT you can shoot it in a 38 special.  There are USPSA shooters who use 38 Short and 38 Long COLT brass to make powderpuff loads. 

If it is 38 S&W Short you can't shoot it from a 38 special.  The case is fatter and shouldn't even chamber in a 38 special.