Camera audio gets confusing because a microphone can be physically mountable and still not be electrically compatible. The mount and the audio connection are separate questions.
3.5mm microphone input
This is a common analog camera microphone connection. A small shotgun microphone or wireless receiver can often connect here, but cable wiring and plug type still matter.
Cold shoe
A cold shoe is only a physical mount. It does not provide power or audio by itself. A microphone attached to a cold shoe usually still needs a cable to the camera.
Hot shoe or digital accessory shoe
Some camera systems provide electronic contacts in the shoe. Compatible microphones can pass power, control, or digital audio through the shoe without a separate 3.5mm cable.
USB-C audio
Some cameras and compact video devices accept digital audio through USB-C. Others use USB-C only for charging or data. Never assume a USB-C microphone will work just because the connector fits.
Wireless microphone systems
A wireless system usually has a transmitter on the speaker and a receiver connected to the camera. Some newer cameras and compact devices can pair directly with compatible transmitters and skip the receiver.
Why headphone output matters
A headphone jack lets you hear clipping, wind, clothing noise, radio interference, and cable problems while recording. A camera can have a microphone input without offering headphone monitoring.