In the pro audio world a processor is an effect, eq, compressor, expander, gate, etc etc.
In the Home Audio world a processor is a 5.1 or 7.1 pre-amplifier usually with delay, basic EQ, independent volume controls, and some type of digital processing.
In the pro-audio world pre-amplifier usually means a gain device for setting input level on consoles or of microphones.
A "preamplifier" usually in the home audio world means a two channel - aka stereo - device which is strictly analog. But, could have a digital input for two channel decoding.