[oaththrowaway]

To purchase a firearm from a store or any "licensed" individual (someone who has an FFL: https://en.wikipedia.org/wiki/Federal_Firearms_License) you must pass a background check done by the FBI. You can read more here: https://www.fbi.gov/how-we-can-help-you/more-fbi-services-an...

If you buy a gun from someone on a classifieds site or friend/family, in most states you don't have to get a background check to transfer ownership of the firearm. This is typically the "loophole" that people refer to when they want Universal Background Checks.

I'm not sure what you mean by buying illegally - whether you mean to someone prohibited from owning firearms (like a felon or something), or buying "illegal" guns... Either way there are usually stiff penalties for owning restricted devices. For example if I were to 3D print an auto-sear for an AR-15 (making it full-auto), that's a ticket to a 10 year sentence in federal prison. Assuming I don't have the permission slip from the ATF. As for prohibited persons buying a firearm, I'm not sure what the penalties are, but at the least it'd be a violation of their release?