It doesn't get much clearer than "all poisons". Why your DM wouldn't count the "magical poisons" and "artificial poisons" sets as subsets of the "all poisons" set is beyond me.
Depends on how much realism vs. magic you want to interject into your game. The obvious/easy choice is to go with whatever the standard rules say, but in case you want to make some homebrew tweaks based on science, here's some boring real world background. Warning: most of you will find this unspeakably nerdy and TL;DR.
Immunity to venom is something that can evolve in the organism as part of a natural "arms race" between predator and prey, which is why you see significant specific antibody activity in local mammal populations that are heavily predated by venomous snakes. The snake population ends up semi-randomly turning on or turning off genes that express various components of their venom, and in some species this can actually be a dynamic/ontogenic process in the individual animal as its size and age moves it to a different prey niche.
Immunity to a specific toxin or class of toxins doesn't carry over to any other class of toxins. Take a mammal from a population with strong immunity to the venom of local rattlesnakes and expose it to a snake from a different geographical area, and it's just lunch. This can even be true for snakes in the same species, as individual and locality expressions of venom components can be highly variable.
Immunity to venom can also be acquired through gradual introduction and the buildup of antibodies, which is why a number of scientists who work directly with the live snakes or with venom or both practice SI, self-immunization. A non fatal exposure leads to the production of antibodies, which can be maintained with regular small subcutaneous injections.
Exposure via the mucosal route is much more likely to trigger the wrong cascade of immune response and lead to sensitivity/allergy rather than increased immunity, which is why folks who work with lyophilized product and herpetologists working with spitting cobras who deliver their annoyance in airborne form are well advised to either wear respirators or do the sub-Q shots. You can avoid a bite, but you can't avoid mucosal exposure if you're in the same room with a spitter when it unloads. Or after it unloads for that matter, if you clean the surfaces. Bleach helps but doesn't eliminate the exposure issue. A number of venom lab workers do the sub-Q shots as allergy shots rather than in quantity sufficient to stimulate significant antibody production.
Raising antibodies to most natural venoms, at least on the reptile end, is pretty straightforward and has only one major pitfall. Neurotoxins and myotoxins are easy. Cytotoxins are the toughie because of tissue death on self injection even of dilute amounts. That's where you start wanting to think about doing protein fractions, which takes it out of the realm of a DIY project or a small venom lab project. Electrophoresis columns are a lot more expensive than lyophilizers. But, it can still be done, albeit not nearly as effectively. In the case of venoms with a strong cytotoxic component that effectively act as a pre-digestive, lysing and dissolving cells, immunization tends to be less effective even when it can be accomplished without injury.
Please note that even if you have good circulating levels of a venom-specific antibody in your system at the time of a bite, if that critter seriously unloads on you, the venom will almost certainly outpace the ability of your antibodies to stave it off. What SI means on a practical level is that you will be able to shrug off minor envenomations with little or no ill effect, and for anything beyond that you will need less antivenom and less time in the hospital, on a respirator or on a drip to prevent rhabdo and kidney shutdown. Not none, just less. Fair warning: the term "immunity" is pretty misleading, because it really isn't. At least not in the real world. "Resistance" would probably be a better description of what can realistically be achieved either through evolution or self-immunization.
Raising antibodies and being sure of triggering the correct IgG vs IgE cascade is definitely do-able for snake venoms. When you move to poisons that work in an entirely different way in the body, antibodies are no longer effective in combating them. There is no antivenom, or effective natural antibodies, for something like heavy metal poisoning. You can administer chelating agents that can bind to those molecules and speed their passage from the body, but I am not sure that there is any way of having a permanent natural circulating level of chelating agents already in the body, as there is with venom antibodies.
There is nothing that can be done to immunize vs corrosive poisons that act directly to cause damage to flesh. You can reverse their continued action after the fact, but the agents you're using may be as damaging to the patient in the absence of any corrosive to neutralize as the corrosive itself.
My knowledge is minimal on the subject of poisons that aren't delivered by bite or sting, but I do know that they have some radically different mechanisms of action and are not affected by antibodies which can be produced by the body. Immunity to injected biotoxins, even a wide range of them, would have no effect on the types of poisons that affect the body by different mechanisms and which are not mitigated by natural antibodies.
Blanket immunity to "poisons" is not a concept that makes any sense medically or scientifically. Which is not necessarily relevant when you're playing a fantasy game, if you simply use the deus ex machina of "it's MAAAGIC" to explain away the discrepancies. In real life, people can't cast Fireball either. So, it's certainly excusable. But if you feel like being a bit devilish with your players and setting limits on anything defined as non magical poison immunity, these would be some reasonable starting points.
TL;DR, just say it's magic and forget about it. Unless you're nerdly enough to care how poisons work in the real world and apply that to your campaign.
