I'm surprised that nobody has pointed out that there are
three ".38 Colt" cartridges.
.38 Short Colt is an older cartridge that has historically been loaded both with heeled outside-lubricated bullets and smaller-caliber inside-lubricated bullets. AFAIK all recent-production commercial ammo uses inside-lubricated bullets in the same caliber as .38Spl, but you might encounter a few aging boxes of outside-lubricated cartridges at a gun show. IIRC it was produced in this form as recently as ~40 years ago; IOW recently enough that it's not necessarily a rare antiquity yet!
.38 Long Colt is a more powerful cartridge that, in its modern form, is almost always loaded with an inside-lubricated bullet in the same caliber as .38Spl. This cartridge is far more commonplace and generally less expensive than .38SC. If you're looking for a low-recoil alternative to .38Spl, IMHO .38LC "Cowboy" loads are your best bet.
.38 Colt New Police is the same thing as .38S&W and/or .38/200 for all practical purposes. The name is the result of a long-ago Colt policy to not put their arch rival's name on their guns.
As other posters have correctly pointed out, this is a slightly larger-caliber cartridge that will NOT chamber or function in most .38Spl, .38SC, or .38LC firearms, and it was NEVER commonly loaded with an outside-lubricated bullet.
[EDIT] .38S&W / .38 Colt New Police has the colloquial nickname of .38 S&W "Short", a name that was never used by either Colt or S&W in any official capacity, but has long been used by store clerks and more recently on the labels of some commercial .38S&W "Cowboy" ammunition to prevent confusion with
.38 S&W SPECIAL CTG., the name rollmarked on older S&W .38Spl revolver barrels. Do NOT confuse .38 Short Colt with so-called ".38 S&W Short"- it's NOT the same thing!