What is the difference between an injected and regular STM32 ADC channel?

You can configure the ADC to read in a sequence of channels in a loop. Those channels are being converted regularly. In injected mode conversion is triggered by an external event or by software. An injected conversion has higher priority in comparison to a "regular" conversion and thus interrupts the regular conversions.

The different ADC-Modes are explained in application note AN3116.

The injected mode is a mode where the ADC conversion can be "injected" during the conversion of regular channels due to some trigger (timer or something else). This is useful, for example in motor control application , to delay conversion until after some event is complete (such as transistor switching) so that the conversion noise is reduced.