These terms seem to have become quite interchangeable, but they actually mean quite different things. There are many types of smoke alarms and smoke detectors, but here is a relatively simple explanation of some of the key differences.
The image below is an example of a smoke alarm. It’s likely to:
be 240V powered;
have a battery backup;
have an alarm incorporated in the device;
found in your house, flat or apartment;and
be interconnected with other smoke alarms to make more noise joined together’

(Image courtesy of Wikipedia)
The image below is an example of a smoke detector:

(image thanks to Pertronic Industries - it's an ionising type detector (Series 20o smoke sensor))
It:
- is not fitted with a battery backup;
- relies on DC power from a fire indicator panel;
- is a “dumb” device connected to a fire detection and alarm system – it sends a signal to a fire panel which outputs a signal to other devices; and
- is likely to be found throughout multi-storey commercial, health and aged care, or residential (as opposed to domestic) buildings in public areas.
I hope this helps clarify what can be a common misunderstanding for the lay and industry person alike!