My Mum and I are both diagnosed asthmatics (both diagnosed in childhood) and use inhalers (I only really need the blue Salbutamol inhaler these days) but my Dad, who is definitely not asthmatic, was prescribed a blue inhaler as he suffers from pretty bad hayfever and his breathing gets affected, so no, an inhaler doesn't necessarily mean you are asthmatic, not unless you are formally diagnosed.
It just helps open the airways when the hayfever is doing it's worst.