Modern law makes a difference between a professional full-time soldier and a mercenary, but historically they were long pretty much one and the same thing; "regular" soldiery were just usually engaged for a longer term. Eg. the post-Marian Roman army was very much a mercenary force; the men, whether citizens in the Legions proper or noncitizens in the auxilia, served for pay and other benefits. Conversely their earlier reservist system worked on basis of legal obligations of the citizenry (and client peoples and states) to serve under arms.
Similarly many of the more "regular" Medieval troops (pretty much all that didn't own land themselves really) were essentially salaried mercenaries, drawing regular pay and upkeep in return of putting their military skills at the use of their paymaster be that now a free city, feudal landlord, monarch or whatever. "Permanent" mercenaries essentially. The faris knight-equivalents of the Middle East were just such salaried standing troops.
That aside, many of the desert tribesmen serving the rulers of the region would also have been essentially mercenaries - even when they were nominally allies, that was often based on rank bribery of the chieftains making their followers mercs-by-proxy. Ditto for the Turkish nomad tribesmen, although I don't know how common they were in Egyptian armies.
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