
In a common cold a person catches a virus, it lasts for about two weeks or so. It is annoying and can involve sneezing, abundant mucous, and a sore throat. A person with a cold doesn't even have to see a doctor because it is a virus. People will urge you to take some vitamin C and zinc for to boost the immune system. All in all, it is annoying, but certainly not as serious as ARDS.
ARDS (Acute Respiratory Distress Syndrome or Adult Respiratory Distress Syndrome) occurs usually because of with widespread infection in the body (sepsis) or as a result of pneumonia, trauma, shock, severe burns, aspiration of food into the lung, multiple blood transfusions, and inhalation of toxic fumes, among other things. It usually develops within 24 to 48 hours after the original illness or injury and is considered a medical emergency. It may progress to involvement of other organs. When ever this happens, it can actually become life threatening. Symptoms which show that someone is going into ARDS is that they have difficulty breathing. The lungs become very stiff. It often is necessary to put someone like this on life support.
A chest x-ray of a set of normal lungs appear black (air appears black). The Chest x-ray of someone in ARDS often appears white. The lungs absorb fluid like sponges and become very stiff and difficult to ventilate. The difficulty of ventilation requires an internal medicine Doctor or Pulmonologist who isn't afraid to try different modes of ventilation.

A person with ARDS who needs to be put on life support will spend a minimum of two weeks on the ventilator. There is no medication that will heal the lungs from ARDS, it is a matter of waiting for the lungs to heal. Supportive therapy is all that can be done. Life support, antibiotics, sedation, diuretics and wait.
Whereas a cold is just that, a cold, which can be a pain, ARDS is a life threatening illness requiring life suport. The difference is that one can be life threatening and the other is just annoying.