Cold-like is literally a cold.
You need to understand infection diseases are **not** defined by the viruses that cause them (usually) they are defined by how they present. You diagnose a cold by your symptoms, if you have the symtpoms you have a cold, that is true no matter what virus happens to be causing it. In fact a cold is causes by so many different viruses that it doesnt even stick to a single family... You can literally have one of any of a thousand different viruses and they are all colds, not just cold-like but actual colds.