Magic is defined as some unusual occurrence for which you don’t see (or are unaware of) the cause. The magic you’re referring to, technically Sihr, also falls into this, i.e. requiring a cause but is more specifically categorized as an unusual or supernatural occurrence achieved with the help of shayateen/jinns through actions that would please them. Among other things, this involves shirk and kufr.
Miracles on the other hand, are supernatural occurrences that have no hidden cause behind them apart from divine decree.
During the incident in Musa (AS) time, when he faced off against the magicians, the magicians knew immediately what he was doing was beyond magic and they believed in him right away.