What are the differences between slow cooking and poaching a chicken soup and how does slow cooking/poaching soup affect salt absorbtion?

Poaching is about cooking something gently, until just done. This is good for chicken breasts: white meat has very little fat and connective tissue, which makes it well-suited to this. It's at its most tender when it's not overcooked. Dark meat will be fine too. As with most other methods of cooking, it just needs to reach the appropriate temperature in the center.

Slow cooking, on the other hand, is about bringing something up to temperature and cooking it there for a long period of time. (There's no temperature to reach - it'll have been hot enough for a long while.) With meat, this is good for tougher cuts, as the long cooking helps break down connective tissue and soften it up. This is amazing for something like a pork shoulder, which can be cooked for hours and hours, until it's completely falling apart. You can probably get some fraction of that effect with dark meat. White meat will be iffy.

As for your favorite topic, salt absorption, longer cooking will get you more penetration into the meat, especially if it begins to fall apart. That won't happen easily with white meat, though, so it'll be a small effect - possibly you could cook it a while then pull it apart with a fork to help. It'll be a bit better for for dark meat.

Finally, since you've posted so many questions asking basically the same thing, my two cents: the best thing to do is probably just to roast chicken (don't overcook it!), shred it, and add some kind of sauce with a decent amount of salt. Cook it a little bit longer if you like, and there you are. You can only go so far with boiling/simmering/poaching/slow cooking, no matter how much you try to optimize it, and you've already gotten the main advice in other questions: possibly tenderize it, cook it in salty liquid, and perhaps help pull it apart once it's mostly cooked.