The drachma is the Greek word for a unit of weight that was the currency of the Byzantine Empire. It was used not just in Byzantine territories of Egypt, Anatolia and the Levant, but through commerce, across the greater Middle East, where it was called the dirham. The dirham was widely used at the time of Mohammed’s conquests of the Middle East, and despite the engraved images that appeared on the coin (prohibited by the iconoclastic Muslims), it continued to be used in the first Caliphate, with some places copying the style and form of the currency to issue their own coins. In Arabic, the word dirham was used for the actual Greek currency used in circulation, whereas money issued locally based on the drachma was called a dinar, based on the the Latin word denarius, which ultimately had the same linguistic root as the drachma.
Today, that distinction is historical trivia, but currencies in many Middle Eastern countries are still called dinars and dirhams, often together with Fils, an Arabic word that historically meant coin or a small unit of weight; and the Rial (or Riyal), a currency that emerged in the last few centuries.
Currencies used today.
In North Africa, the Moroccan dirham is subdivided into 100 santimat, a subdivided currency unheard of anywhere else in the world, the Algerian dinar is subdivided into 100 santeem, the Libyan dinar is subdivided into 1000 dirhams, and the Tunisian Dinar is subdivided into 1000 milim. Both Morocco and Tunisia used the Rial during Ottoman times, which was locally issued by the local governors.
Jordan and Iraq use Dinars, Dirhams and Fils. In Iraq, 1 dinar is equal to 100 dirhams and 1,000 fils (although there are more than 1,000 dinars to the dollar, so its unclear if the subdivided currencies are needed anymore). Jordan is slightly different — 1 dinar is equal to 10 dirhams (not 100) and 1,000 fils (same as Iraq).
The rial (or riyal) was probably based on the Spanish Real, and first emerged as the currency issued by some governors in Ottoman possessions. Today, it is most commonly used in the Arabian peninsula. The Iranian rial is subdivided into 100 dinar, and was first introduced in 1798 as a coin worth 1250 dinar. The Riyal is the currency of Saudi Arabia and is subdivided into 20 Ghirsh or 100 Halalas, and in Qatar the Riyal is the currency. The Yemeni Rial is subdivided into 100 fils, but before unification, North Yemen used the Rial and South Yemen used the Dinar. The Omani Rial is subdivided into 1000 baisa.
Arab countries excluded from this map include Egypt, Sudan, and Syria, which call their local currency pounds, based on the British sterling. Lebanon uses Francs.
Confused? This is actually a condensed and very summarised overview. If you want to read more, check out the wikipedia article on the historical use of British currency in the Middle East, where you can try and wrap your head around all the intertwined narratives of what currency was used when, and why. Every country in the Middle East used several forms of currency in the last century, from pounds to rupees to shillings to dinars to rials. Fun trivia includes: Qatar and Dubai once had their own currency union; Omani Riyals and Jordanian Dinars are currencies that descended from the pound sterling, despite their different names, and the value of one Omani Rial and one Jordanian Dinar is similar to one British Pound even today; the currency units in Saudi Arabia, Qatar, and the UAE remain very similar in value today because they descend from units the Maria Theresa thaler, a currency from the Austrian Empire.