You are correct. Many (but not all) viruses stimulate a similar immune response as with the flu. Then you feel "flu like". In truth, not all flu's are caused by the flu virus. There are other viruses that can create similar symptoms to the flu. Most of the time we just don't go and check every patient, and it resolves much as the flu does. But the immunological response is similar causing similar symptoms. Same with colds by the way. Most people think there is a "cold virus". Actually colds are caused by multiple different viruses. Rhinoviruses may cause 50% or so, but what most don't realize is maybe 25% are caused by corona viruses. Yes, same family as SARS-CoV2 but a bit more distantly related at a genetic level. But the symptoms are that of a common cold. The common cold has the added symptoms of a runny nose, which again is a function of the immune response to the virus, not caused by the virus itself.