No, they are not all the same. Most firearms makers prior to WW2 or so had proprietary cartridges of their own design, and there was no such thing as standardization. Reading through your listed cartridges I offer the following:
1. .32-20 is the popularized (and SAAMI standardized) reference to the .32 Winchester Center Fire cartridge, first offered in the Model 1873 Winchester rifle, later chambered in most other makers' rifles and quite a few revolvers (including the Colt Single Action Army).
2. .32 WS (Winchester Special) is a rifle cartridge adapted first to the Model 1894 Winchester rifle. Quite similar to the .30-30 (.30 WCF), but utilizing a .32 caliber (8mm) bullet.
3. .32W could possibly refer to either the .32-20, the .32-40, or the .32 Winchester Special. More information would be needed.
4. .32Win, same comments as above.
5. .32 WCF generally refers to the .32-20, as its original name by Winchester.
6. .32 New Police is a revolver cartridge offered by several gun makers. Rimmed cartridge of moderate capacity and performance.
Gun makers tried to cater to gun buyers' wants, frequently providing guns chambered for popular cartridges originated by other companies, but not wanting to acknowledge another company's name. Thus .32 WCF became popularized as the .32-20, .38 WCF became the .32-40, .25WCF became the .25-20, .30 WCF became .30-30, and so forth. A complete listing would be nearly endless.
To the best of my knowledge, none of the cartridges you have listed are the same. All are different. Some are rifle calibers, some are handgun calibers, and some have been used in both roles.