In common usage, there is a difference between processors and effects. In general, processors "process" the entire signal, while effects usually "effect" only a fraction of the original signal.
Processors include compressors, limiters, gates, EQs, exciters, de-essers, stereo width adjustors, autotune, etc. Effects include reverb, delays, phasers, chorus, flange, etc.
A basic mic preamp only has a few features. Its basic function is to raise the very low mic level signal to a line level so that a mixer, tape deck, or any other gear can easily utilize it. Other features most mic preamps have are phantom power, polarity reverse, and often a pad and/or a low cut switch. Usually, but not always, there will be some sort of metering, or at least a clip LED.
Optional features on a mic preamp include a 1/4" DI for plugging in an instrument and impedance options.
But many mic preamps can also include some processors built in. That could be some parametric EQ, or some limiters. When they include a whole string of processing options, the mic preamps essentially become a channel strip (like in a mixer). There are many mic preamp/strips sold today that have compression, gating, de-essing, EQ, and limiting all in one box.
