On the serious side, Farside,
rest means exactly that - being able to rest, recline if you desire, and sleep, if you so wish. Thus you would need a replacement to occupy your seat, as it is obviously NOT possible to achieve rest while confined to a flight deck seat.
relief means taking some form of relief from your duty - whether it be simply reading, pushing the seat back and taking a few zzzz's [if you are the type who can], or taking a walk through the cabin, or a visit to the loo.
There is a big difference between the two. Rest obviously being of such time, as to require another similarly qualified pilot to carry out any duties required during your absence [eg. fuel monitoring and x-feeding, weather avoidance decisions, level changes,ATC restrictions, handling of unruly pax, crew incapacitation, or/and emergency procedures with associated decision making].