Many of the symptoms caused by allergies are also similar to food poisoning. This is especially true of stomach upset, diarrhea, and unpleasant side-effects along those lines (see gluten allergy symptoms for some specific examples).
With the possibility of having identical symptoms, how do you know if you really have allergies, or if you are dealing with food poisoning?
First of all, the allergy symptoms are not identical to food poisoning symptoms in most cases. There are often other effects that are not the same as food poisoning.
The main thing to watch out for are the patterns of when you experience the symptoms.
In most cases, food poisoning is a one-off thing. Someone left the meat out of the fridge for too long. The food was contaminated during processing. One of the ingredients went bad, and was added to the dish unnoticed. There are many causes for food spoilage, but they are usually not consistent. In other words, do not expect that since you got food poisoning from the left-overs last week, that you will get sick every time you eat left-overs.
There could be exceptions. If a particular food processor has poor hygiene standards, or there is a fault in the way food is handled, there could be a raft of consistent food poisoning cases.
But even this is unlikely to be confused with food allergies. First of all, many people will get sick from the same food, but only if from that particular source.
Besides, most first-world countries have food inspection agencies that would discover and stop such problems pretty quickly. In the third world, food tends to come from a large number of small suppliers, so you would expect to experience food poisoning randomly (and more likely from bad water than bad food).
Allergies, on the other hand, tend to cause consistent symptoms in an individual, but not those around them. Even the symptoms themselves vary from person to person, even for the same food allergy.
This is true of allergies and food intolerances.
If you are sick for years on end, suspect food allergies. If you are sick occasionally, suspect food poisoning or some other cause.