Are high pass/low pass filters FIR filters?
The expressions Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) refer to the time-domain response of the filter. When an impulse is fed into the FIR filter in the time domain, it's response goes to zero within a finite amount of time. The response of the IIR filter does not.
Low Pass Filter (LPF), Band Pass Filter (BPF), High Pass Filter (HPF), Band Stop Filter (BSF) and Notch Filter (NF) are expressions that refer to the frequency-domain response of the filter - which frequencies it passes, stops or attenuates.
Both domains can be used to classify a filter's behavior. You can implement a LPF as a FIR filter. In the frequency domain, it will pass low frequencies and stop high frequencies. Simultaneously, in the time domain, the impulse response of the filter will return to zero after a finite amount of time. You can also implement a LPF as an IIR filter. It will have the same behavior in the frequency domain, but its impulse response will never reach zero in the time domain.
The filter's response in the time and frequency domains complement each other.
I hope this helps.