Is the word “pray(er)” different between Christians and Muslims in your language(s)?

I’m guessing rather than certain here, but Muslim Greek and Jewish Greek, as spoken by longstanding religious communities, did have distinct vocabulary about religious practices, and I’d have no reason to think prayer is an exception.

The two Turkish terms given in Murat Öz’s answer are namaz and ibadet. As noted in Τι είναι το Ναμάζι;, ναμάζι is frequent in Greek literature with reference to Muslim prayer, and has been used in the Greek press.

The one instance of ibadet in Greek I find on line is in a letter from a Greek bishop in the region around Drama, written in 1911 and available at Μικρόπολη Ιστορία Οθωμανική Περίοδος και Τουρκοκρατία Μικρόπολης Καρλίκοβα Δράμα Mikropoli Mikropolis Karlikowa Καρλίκοβα Μικρόπολη Μικρόπολης. It disapprovingly cites a local Bulgarian Orthodox (“schismatic”) cleric referring to Orthodox prayer as ιμπαντέτι; the Bulgarian is cited (in vernacular Greek with Turkish codeswitching) as saying “I am liberal: I would be happy to celebrate mass with the bishop. I ask no-one for permission about ibadet, neither the Exarch [Bulgarian church leader] nor anyone else, I’ll even yaparım ibadet [do prayer] with a hoca [imam].”

The call to prayer, adham, is referred to through its Turkish form ezam > εζάμι in the Greek press still, with reference to calls to prayer not only in Turkey, but also in Jerusalem.