To the OP:
9mm and .380 are very different guns. Most .380 are direct blowback, which simplifies their design and production, while most 9mm pistols are delayed blowback, generally with a tilt barrel, which enhances reliability and durability, in addition to allowing them to handle the 9mm round.
9x17 (AKA .380 Auto, 9mm Browning, 9mm Corto, 9mm Court, 9mm Kratak, 9mm Kurz, 9mm Scurt, 9mm Short, 9x17mm) - mostly small pocket pistols. .380 is a decent round, there are some old venerable guns chambered in it and some interesting new designs. If I was going to carry a .380, I would pack a Kel-Tec. (but then, if
I was going to CC a KT pocket pistol,
I would buy a P32)
9x18 (AKA 9mm Makarov, 9mm Soviet, 9mm russian, 9mm Mak, 9mm PM) - slightly larger than the .380 - slightly larger surplus pistols in this caliber are quite inexpensive and concealable.
9x19 AKA 9mm Luger, 9mm NATO, 9mm Parabellum, 9mm Para, or simply "the nine" - full power pistols, almost all with John Browning tilting barrel designs. 9mm pistols in smaller sizes are more expensive, more finicky, and often higher maintenance.
There are a
plethora of other 9mm diameter rounds out there, but those are the most common.
If you really must have a small and slim 9mm pistol, the
Kahr,
Kel-Tec,
Walther, and
Taurus lines all have a model or two, but they are all marginal for pocket carry. Rent a few and see what you like, and then work your carry method around that. There is a reason that IWB carry is so popular, it is well concealed even with larger guns, the weight is on the belt and spread out more than in a pocket, and the draw isn't hampered by a pocket overfilled with gun, hand, holster, and the mouth of the pocket. The only true pocket 9x19 guns I can think of are the
Rohrbaugh (expensive!), and the
Boberg (not on the market yet)
You may have to get over your dislike of polymer if you want a small pistol in a heavier caliber. Have you even shot any of these pistols you dismiss out of hand without real consideration?