How is clock bus different than peripheral clock in STM32?
What do you mean when you say "peripheral clock"?

A peripheral is fed the clock of whatever bus it is connected to, the PLL, oscillator, or system clock (selectable for some peripherals and fixed for others). It may or may not use this clock as to run a portion of, or the entire peripheral.

This clock may subdivided to run slower circuitry inside of the peripheral which may or may not manifest externally to the peripheral. This may happen multiple times and at multiple levels in the same peripheral.

For example, a UART might run off a 48MHz bus clock. But the UART might transmit and receive at 1Mbps. But a UART 8x oversamples received signals so some part of it must run at 8MHz. All these are subdivisons of the bus clock.

A sigma delta ADC might step the bus clock down to run the decimation digital filter which uses multiple samples to construct a single output reading, step clock down yet again for the actual sampling (oversampling), and step that down yet again for the actual output (though this would be tightly linked with the decimation filter clock if it is even separate at all).

Similarly, a SARs ADC has a sampling clock, and a faster clock that does the actual cap charge redistribution on each sample to figure out the bits before the next sample comes in, and ultimately the even faster bus clock from which the first two originate.

Hopefully you can understand now why it is vague when you ask "what frequency the peripheral operates at?" without getting specific about what exactly you are referring to.

Personally, when I say "peripheral clock" (the STM manual does this too I believe), I am referring to the clock feeding the entire peripheral from the bus, PLL, whatever. Everything past that is something like "the sampling clock" (for an ADC) or the "serial clock" for the communication bus itself. There is only one clock for the peripheral so I call it the peripheral clock, but there can be multiple clocks inside the peripheral. These are not usually referred to as clocks though.