Pre-emphasis is spectral shaping at the tx to compensate for the spectral shape (LPF sort of) of the comm channel.

In SerDes, that can be seen in the time domain, by amplitude boosting the transient edges of the signal.

PR = partial response - usually means bandwidth limiting the receiver input to reduce noise content. However, that also means reducing the higher harmonic content of a signal, thus the term "partial" response.