Li7 nuclear spin-lattice relaxation rates (R1) versus the temperature at several resonance frequencies (4 to 40 MHz) are reported together with the conductivity measurements, σ(ω), in the range 1 Hz to 3.76 MHz on 0.56Li2S+0.44Si2S, a glassy fast-ionic conductor. Both R1 and σ(ω) are fitted consistently over the whole temperature and frequency range by using a stretched-exponential, i.e., exp(-t/τ*c)β for the corresponding correlation functions (CF). Formulas that relate R1(ω) and σ(ω) and that give the asymptotic behavior as functions of T and ω of both quantities are tested experimentally. We find significant differences between βσrelated to σ(ω) and βR related to R1, which implies a difference in the corresponding correlation functions of the ionic diffusional motion. An apparent order-of-magnitude difference in τ*0 attempt times was derived from these conductivity and NMR measurements. The implications of these findings are discussed in terms of the microscopic mechanisms which lead to fluctuations and relaxation in fast-ionic conductors.