The Difference between the Three Inputs
What differs between them is the signal intensity, so-called signal level. There are basically four types of signal levels.
The microphone signal has the weakest voltage, typically just a few ten-thousandths of a volt. But it will vary slightly when the speaking distance changes.
The instrument level typically comes directly from a guitar or bass. The signal intensity increases significantly when it reaches a line-level, or so-called 1-volt signal, which is approximately 1,000 times stronger than a mic-level signal.
The AUX level, which is near the line level, can be used to find the AUX jack of some Bluetooth speakers or computer sound cards.
The speaker level. It has a much higher voltage than line level and requires speaker cables for safe signal transfer.
How does the audio signal transfer?
The microphone signal that travels through pre-amp, mic-to-line amplifiers, or mixer(most commonly used) could become a line signal.
What device and what kind of jack should I plug a mic into?
If you want to input an analog microphone (except USB mics) to a computer or speaker with only a line-in jack, you will need a pre-amp, an amplifier, or a mixer.
The misconnection will cause great harm to either audio quality or devices. Plugging a microphone directly into a line-level input will result in almost no sound because the mic signal is so weak that the line input cannot hear it.
Connecting a line-level source (such as a mixer output) to a mic-level input will cause the sound to be loud and distorted because the line signal is much stronger than what the mic input will accept.
As for an instrument, you could also use a DI box (Direct Injection or Direct Input) to take it to line level. The AUX signal is always unbalanced. So microphones will not work properly or not even work at all if connected to an aux input.