Alarm call, wake-up call, and morning call all refer to being woken at a set time, but they differ in context. An alarm call is specifically a phone-based service arranged through a hotel or operator. A wake-up call is broader — it can be any call that wakes you, including a friend phoning to make sure you are up. Morning call is common in East Asian hotels but less used elsewhere. An alarm clock is a device that sits on your bedside table and rings; it is not a service. 'The hotel gave me an alarm call at 6 a.m.' — you would not use alarm clock here because a person, not a machine, is doing the waking.
Alarm comes from the old Italian phrase all'arme, meaning 'to arms!' — a cry to prepare for danger. Call comes from Old Norse kalla, meaning 'to shout or cry out'. The compound alarm call entered English hotel vocabulary in the early 1900s, when telephone switchboard operators would phone guests' rooms at a requested time to wake them.