Some critical differences between the situations that come to mind:
- The problem of counterfeit currency is well acknowledged and has roots in antiquity. Reasonable people agree that currency genuinely cannot do its only job if counterfeiting is possible, and have had that agreement for thousands of years. In addition, the sole right to print currency is given to the US government in its constitution (almost certainly for this reason). These two things grant government control over printing currency both a moral and a legal legitimacy that government control over printing gun parts doesn't have.
- Because the government has control over the design of legitimate currency, it is actually practical to prevent software from reproducing it. See: https://en.wikipedia.org/wiki/EURion_constellation . Gun parts have no such distinguishing characteristic, and cannot be made to have one, since there is no authoritative body responsible for all of them. Having such a marking could be made legally mandatory, but it is not actually required for the function of the part, whereas currency needs to match the authentic design in order to be useful. It is therefore much less practical and effective to mark gun parts to prevent replication than it is to similarly mark currency.
- Creating your own guns specifically (and weapons, generally) is widely seen as a natural or God-given right. I would go so far as to say that it is intrinsically human, and that losing access to it would be as painful to some as losing access to rock 'n roll. I would say that due to this pain, losing that right is one of the chief signs of an enslaved people. While not everyone would agree with me, many would, which gives the issue a divisive moral edge. By contrast, creating your own currency might be seen as some sort of natural right by some people, but creating your own US Dollars certainly is not seen that way by anybody. Well, I'm sure you could find someone, but you know what I mean.
- As far as I know, there is no law compelling printer/photocopier manufacturers to use anti-counterfeiting software, and compliance is voluntary (but apparently pretty widespread -- though I doubt it's universal). A similar voluntary setup with 3D printer manufacturers would be less objectionable (though also much less likely to succeed). Introducing any sort of mandatory compliance regime introduces friction, slows innovation, and invites corruption.
- Manufacturing gun parts is actually pretty easy, and could be accomplished via many methods accessible to hobbyists, ranging from whittling by hand to duct taping hardware together to lost wax casting to desktop CNC to a desktop injection molding setup to metalworking on a lathe in a garage machine shop. It is in no way limited to 3D printing, though that admittedly lowers the bar a bit. Learning to work on guns is not significantly harder than learning to work on cars, though perhaps fewer people know how to do it. Thus, a focus on 3D printing seems much more driven by sensationalism, paranoia, and ignorance of this fact than it is by practical assessment of the issue. By contrast, creating even minimally recognizable counterfeit currency without the assistance of a computer is practically impossible and certainly cost-prohibitive. In manufacturing gun parts, it is perfectly practical in some cases to do the equivalent of drawing a dollar bill with a crayon -- something much less successful in the counterfeiting world.
- Adding broad pattern-recognition controls to a 3d printer is a novel and difficult problem that will likely impact innocent people doing legal things. Preventing the printing of accurate-looking currency has a much more narrow impact, and is much more focused on people doing illegal-adjacent things.
Without meaning any malice toward your question, I mention that I write because you have stepped on one of my pet peeves: it seems to me that an inability to see the difference between things that are, in fact, different, is one of the major failure modes of modern society in general. We need an appreciation for texture and nuance if we are to navigate the world rightly.