Signal integrity covers all the issues about single ended and differential signal propagation from the transmitter to the receiver, including problems such as impedance control, discontinuities, reflections, topology, terminations, losses, ISI, jitter, eye diagrams, cross talk and ground bounce.
Power integrity covers all the issues associated with supplying low noise DC voltages to the active devices, and all the interconnects in the power distribution network (PDN) from the VRM to the on-die rail. This includes on-die capacitance, package lead inductance, on-package decoupling capacitors, multiple plane cavities, on-board decoupling capacitors, bulk decoupling capacitors, VRM design, parallel resonance structures and interactions in the entire PDN ecology.
EMC/EMI covers all issues related to passing an emissions or susceptibility certification test. This includes topics related to the test specs, shielding, spectrum control by filtering or clock modulation, the use of ferrites, return path control, suppressing plane resonances, antenna design, sources of ingress and egress of radiation, and use of special materials.