Audio Interface vs Mixer? Which one is best for you!

The common question when setting up a studio is whether you should get a mixer and an audio interface or just an audio interface.
What is an Audio Interface?1
An Audio Interface is a device that connects your Microphone or any other audio source like an instrument to your computer and lets you convert the analogue audio source to a digital format to record in your Digital Audio Workstation (DAW)
Generally, the consumer end audio interfaces have built-in preamps, a headphone out for monitoring and outputs for monitor speakers. The higher-end audio interfaces with multi inputs may have a few microphone preamps for some inputs but not all
“The Audio Interface is designed for just studio use, while the mixer is primarily designed for live use.”
What is an Audio Mixer? 2
The job of the Audio Mixer is to accept and combine/mix, various audio sources and process them. The adjusted audio signal is sent to the output with can be amplified and sent to speakers.
There are two types of audio mixers, the analogue ones and the digital ones. Some of the analogue mixers have a built-in audio interface that lets you connect the final output of the mixer to a computer. They generally have a 2 channel mixdown only.
The digital mixers on the other hand have an audio interface built-in and can give out multi-track audio to your DAW. They also allow you to use various compressors, limiters, EQ etc on each channel of the audio if required.
The primary use of the mixers is for live performances and not to be used in a studio. Though there are mixers from Presonus, Zoom can be used for both live and studio.
So what should you use in the Studio? Audio Interface or Mixer?
The Audio Interface is designed for just studio use, while the mixer is primarily designed for live use.