An audio interface and a mixer serve different purposes in a audio recording or live sound setup.
An audio interface is a device that connects your computer to various kinds of audo equipment, like microphones, guitars, and speakers. It provides a means to convert the analog signals from these devices into digital data that your computer can process, and vice versa. This is essential for recording audio onto a computer or using a computer to process and alter audio.
A mixer, on the other hand, is a device that takes multiple audio signals, adjusts their levels and frequencies, and then combines them into a single or multiple output signals. It allows you to balance the levels of different inputs, apply equalization and other effects, and send the resulting signal to various outputs. In a live sound setting, a mixer is often used to manage the signals from multiple microphones and instruments to create a balanced final sound that’s then sent to the PA system