What's the difference between having asthma and bronchitis?

Infection. Bronchitis is usually caused by a viral infection and causes inflammation of the airways associated with cough and sputum production. There is typically no wheezing with bronchitis. Asthma is also due to inflammation and may worsen with viral infection. Asthma causes cough and sputum production and usually also causes wheezing.
Difference.... Acute bronchitis is an infection of the airways and chronic bronchitis is a form of copd. Asthma is a disease characterized by recurrent episodes of reversible airway obstruction whereas chronic bronchitis has irreversible airway obstruction. Asthma exacerbation can be caused by acute bronchitis, among other things.