Answer:
Thank you for the thoughtful question. You bring up an excellent point that there are several disease processes on the differential for respiratory distress, stridor and wheeze. In these cases, the whole clinical picture (history, physical exam + prioritizing treatment of life threats) needs to be considered.
In the patient you describe (we are assuming they are <8 years-old meeting the Condition for the Croup Medical Directive) with severe respiratory distress, stridor at rest, barking cough and history of recent URTI; priority is to the treatment of Croup with nebulized epinephrine. The history and physical exam findings point more to this condition and given the severity of symptoms, this life-threat that should be considered first.
Should the patient not improve, you may then decide to treat with salbutamol, per the Bronchoconstriction Medical Directive
Notably, a mild expiratory wheeze may be heard in patients with croup even without a history of asthma. However, this is especially true in patients with a history of asthma, wherein the virus that is causing inflammation of the upper airway (giving the barking cough and stridor) can also affect the lower airways giving concurrent wheezing.