In regard to pistol caliber AP - the federal law very specifically and only, states 4 main points -
Commercial manufacture is restricted (to those with an FFL-10),
Commercial importation is restricted (to those with an FFL-11),
Commercial transfer of pistol-caliber AP by an FFL must have information recorded by the FFL
Possession by a person committing a violent crime or drug-trafficking will result in a mandatory minimum federal sentence of 5 years (in addition to whatever other crime they are convicted of).
When you dig deep into the nooks & crannies of the 1986 law and all of the subsection definitions, they actually get surprisingly specific with everything as far as what the restrictions are limited to. For instance, it is 100% legal for a non-FFL person to, say - build 100 or so (or any smaller non-commercial quantity) AP pistol projectiles, load them, use them, or sell a few to another person (on the federal level). This is because they are not “engaged in the business of” manufacturing them “for pecuniary gain” as described in the 1986 law.
As for the state laws, most all states have no relevant restrictions at all. Only CA, IL, TX, and Washington D.C. have what amount to a “ban”, but the laws are virtually unknown - especially in gun-friendly Texas. Four other states have near-bans, or partial bans which are even less known laws, they are: FL, RI, KY, and NJ. In all of these states, the state laws are worded in a way which respects Ex-post-facto, meaning anyone who possessed the ammunition in question before the laws went into effect may continue to possess the ammunition. Also, in Florida or Rhode Island, the ammunition must be “truncated” to qualify as being restricted, which sort of limits the laws’ usefulness to restricting only KTW or maybe a few other random loads. Any round-nose FMJ steel-core penetrator would apparently be fine, and this illustrates just how little the anti-gun type politicians who pass these laws know about guns & ammo.
Aside from those 7 states and the D.o.C., there are 7 other states which have restrictive laws geared very specifically to “Teflon-coated” pistol AP ammo only, which obviously only targets KTW ammo, and which even fewer police or anyone at all knows about. These anti-Teflon laws are a result of the hysteria of the NBC farce of a Nighttime News segment called “The Killer Bullet” which aired in 1982 and set a bunch of anti-gun politicians up to look like fools as they raced to restrict this dangerous new “cop-killer”… which nobody outside of the industry had ever heard of until NBC tripped over itself to produce the garbage with a fraudulent liar named Arthur Kassel (impersonated a federal agent and lied about his qualifications), producer Beth Polson (conspired with Kassel to entrap Paul Kopsch - an effort which failed and which Kopsch later described in Congressional testimony), and the rambling NBC reporter Jack Perkins - who plain didn’t know what he was talking about in the report as he alerted scores of potential criminals to the fact that the ammo existed (which they could never acquire anyway), but more importantly that many officers were starting to wear body armor - a little known fact at the time. The first politician to race to the podium and champion the bill was a democrat NY Rep named Mario Biaggi… who would later be convicted on unrelated federal conspiracy racket charges - a real all-star team there.
The anti-Teflon states are: HI, AL, IN, KS, NC, SC, and OK, but you wouldn’t know even if you asked all the police, D.A.'s, and politicians you could find since none of them knows the law exists.
Aside from that nonsense, you have Louisiana which requires that a person obtain what amounts to a permit from the state police to possess or transact pistol caliber AP ammo, in sort of a “shall-issue” licensing type of way, but I dare you to call them and see if they have any idea what you are talking about - they likely wont, and you shouldn’t bother. Meanwhile in Nevada their peculiar law only restricts the sale of such ammo, but not possession.
There are a handful of other states which might appear to have a law restricting pistol caliber AP ammo, but when you read those laws closely, you find that they are sort of non-laws in that they only apply to when a criminal uses such ammo during the course of a crime, and thus they are only prosecution multipliers, and do not apply to normal people possessing or transacting the ammo.