Are .32-20, .32ws, .32w, .32win, .32wcf and .32new police the same cartridge? If not all which one's are the same?
thanx.

32-20 & 32WCF are the same (WCF = 'Winchester Center Fire')
Found chambered in both handguns and rifles

32win, 32WS,,32W(see edit below) are all abreviations for 32 Winchester Special
A rifle cartridge most commonly found chambered in the Winchester Model 94 LeverAction rifle but also chambered in some Marlin models and other rifles over the years.
***edit: 32W was Marlin's caliber marking for the 32-20 (32WCF) caliber on early Model 1889 lever action rifles,,probably others. They also used 44W (44WCF) and 38W (38WCF)

32 New Police is a revolver cartridge. It is Colt's named version (loaded w/a flat nose bullet) of the 32 S&W Long cartridge.
The latter usually loaded with round nose bullet.

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.

Early S&W .32-20 revolvers will have "32 Winchester" as a barrel caliber stamping. It is the same cartridge as the .32 WCF and .32-20, and both those barrel stampings are seen on later guns. This is probably the .32 Winchester or .32 W you asked about. As previously stated, the .32 Winchester Special is a rifle cartridge similar to the .30-30 except for bullet diameter, but the two are not interchangeable.

Colt was sensitive about not stamping anything on their guns which included "S&W". So Colt called the .38 S&W Special the .38 Colt Special, the .38 S&W the .38 Colt New Police, and the .32 S&W Long the .32 Colt New Police. And the ammunition manufacturers went along with this in their box labeling and headstamps, even though the S&W and Colt cartridges mentioned were essentially identical and interchangeable.