The .32 Colt New Police and .32 S&W Long are the same exact cartridge.
The .32 S&W (not "Long") is a different, shorter cartridge.
I believe, based upon each cartridge's dimensions, that you could fire .32 S&W cartridges in a .32 S&W Long chamber. However, the result would probably be somewhat inaccurate, and the chambers hard to clean afterward.
The .32 S&W Long's rim is a slightly different thickness from that of the .32 S&W. That might cause problems too. Or maybe not.