What is the relationship between asthma and allergy? How to differentiate between them?

Asthma vs allergy. Asthma is a lung disease with increased irritability and inflammation. In many asthmatics much of the underlying inflammation is caused by being allergic to one or usually multiple allergens. Therefore avoiding exposure to or decreasing sensitivity (immunotherapy) to those allergens decreases the information and irritability of the lung making control easier.
Overlapping symptoms. A patient with asthma has their own set of triggers that cause symptoms. Allergies can be one of those triggers. Smoke is a general irritant to almost all asthmatic airways, while exercise, virus infections and acid reflux can also be triggers for individuals. Excellent asthma management involves use of needed asthma medicines plus control or avoidance of the patient's own triggers.
Asthma and allergy. . Asthma causes ' wheezing' --- due to broncho-constriction. Whereas allergies--- cause runny nose, non-wheezing cough, watery eyes, stuffy nose. Etc. Allergies can involve three different systems--- upper respiratory; skin; and/or GI tract. Asthma only affects lower respiratory tract. Now having said so--- asthma and allergies are related---- one can trigger other and both can coexist in same patie.