Standard (minimum-phase) EQs shift the phase of the signal, which is part of how they achieve their frequency shaping. Linear-phase EQs separate magnitude and phase processing, keeping the phase response flat. This is ideal for mastering (where preserving the stereo image is critical) and for parallel processing (where phase shift between dry and processed signals causes comb filtering).
The cost: linear-phase EQs introduce latency (10–50ms) and cause pre-ringing — a faint oscillation before transients. For most mixing tasks, minimum-phase EQ is perfectly adequate and introduces no latency. Linear-phase EQ is a specialized tool for specific situations.