  We revisit the concepts of spin relaxation and spin decoherence of two level
(spin-1/2) systems. From two toy-models, we clarify two issues related to the
spin relaxation and decoherence: 1) For an ensemble of two-level particles each
subjected to a different environmental field, there exists an ensemble
relaxation time $T_1^*$ which is fundamentally different from $T_1$. When the
off-diagonal coupling of each particle is in a single mode with the same
frequency but a random coupling strength, we show that $T_1^*$ is finite while
the spin relaxation time of a single spin $T_1$ and the usual ensemble
decoherence time $T_2^*$ are infinite. 2) For a two-level particle under only a
random diagonal coupling, its relaxation time $T_1$ shall be infinite but its
decoherence time $T_2$ is finite.
