Sensitivity and allergy both have too many meanings, even within the medical community.
It helped me to learn about IgG, IgA, IgM....immune response. This seems the best way to think about it we have at this snapshot in history.
Sometimes the body encounters a threat so great, it turns off all the stupid nonessential stuff like brains, lungs, etc. Saves our lives when falling through the ice into the river, not so great when it's just peanuts. Other times, the body knows something is a threat, but not so urgent. For this, it uses a different immune response like for an injury. Change thickness of blood to wash or clot wound, send army of inflammation dodads to fight off primary infection, put autonomic fight or flight system on red alert in case we need to send the body into full shock... great for wounds, not so fun for irritating bowels. And sometimes the body can treat foods as a low grade threat or can engage full on projectile expulsion to make the toxin get out as quickly as possible. These types can sometimes be measured in the blood with the IgG, IgA... thingies.
The body is really nifty that way. It has about a thousand ways to respond to threats (or perceived ones) and we only know how a handfull of these work.