origin of κουρδίζω may be different, https://el.wiktionary.org/wiki/%CE%BA%CE%BF%CF%85%CF%81%CE%B4%CE%AF%CE%B6%CF%89
in my opinion saati ayarlamak is more convenient. kurmak is more used in setting the alarm (alarmı kurmak). some people may even use the phrase 'saati kurmak' for setting the alarm.
however saati kurmak and saati ayarlamak are still interchangeable. if you set the date you should say 'tarihi ayarladım'
"saati kurmak" and "saati ayarlamak" are not always interchangeable. saati kurmak is only adjusting the time on your clock/timer, saati ayarlamak can be this, and also arranging the time for a meeting, and also setting it to the correct time (e.g. adjusting it to summer time)
@dieprinzessin: kurmak, so this sentence, can only mean the first one, the adjustment of a device (the clock/the alarm) meaning I push a button. Similarly, setting the CLOCK, does not mean "making an arrangement/appointment I set the time for breakfast/ I set the date for the wedding.."
Aren't we talking about to different functions:
the adjustment of a device (the clock/the alarm) meaning I push a button
making an arrangement/appointment I set the time for breakfast/ I set the date for the wedding...
I don't know how the Turkish verbs fit in there. My guess would be kurmak for the first and ayarlarmak for the second.But I am merely based on the discussion above.