There is a spectrum of reactions that your body has to foods, these falling somewhere between allergies, intolerances, and sensitivities.
If you have an allergy, your body perceives (usually) proteins in the food source as a threat and produces anti-bodies/an immune response as a result.
An allergic reaction can be immediate and life-threatening, and the most common allergic antibody is Immunoglobulin E (IgE), but there are non-IgE responses.
The eight common allergens that makeup 90% of allergic reactions are: milk, eggs, fish, shellfish, peanuts, tree nuts, wheat, and soybeans.
An intolerance is a non-immune response and results from foods being poorly digested or absorbed. The symptoms can start within a few hours and last a few days, and are digestive-related (bloating, nausea, cramps, diarrhea, constipation, etc.).
Symptoms of food sensitivities can vary and can often appear unrelated to the food you eat - flying under the radar - and in cases showing no symptoms for days. Brain fog, depression, anxiety, weight gain, sleep, acne, mood, hormonal issues... to name a few.
The common reaction antibodies to food sensitivities are Immunoglobulin G (IgG) and Immunoglobulin A (IgA), which are termed "delayed response reactions".
IgG is the most common antibody found in your blood which "remembers" infections you've previously fought and are deployed when they arise again (in layman's terms), and IgA is found in our mucus membranes and helps to fight bacteria and viruses.
With enough exposure to certain foods, the protein contained in them can also become "invaders", and thus a sensitivity can be developed - which is why variation and rotation of food sources are so important.
For example, gluten. If you expose yourself to gluten for long enough in enough quantities it will eventually lead to sensitivities. (Source: Dr Mark Hyman and co.)
Allergens can be tested for, but tests for intolerances and sensitivities are less accurate so elimination diets are often used - again, a topic for another day!