Transient and frequency solver is like FDTD vs FEM. Frequency domain FDFD and FDTD it is only solver mode. MWS is particularly using the FIT method (Finite Integration Technique), the brother of the FDTD method. Those two techniques are similar but not identical.
One more difference in extended form is Time Domain Solver - good for big structures (less memory hungry), arbitrary excitation signals (like square waves or pulses), broadband problems frequency Domain Solver - good for small problems (like RF-CMOS structures), use of Floquet Modes applied to non-normal incidence (on Frequency Selective Surfaces), low frequency applications (like RFID for the kHz-range) and very high Q-filters (if simulated in time domain require a huge time to get it done). Both solvers are original from the FIT - Finite Integration Technique - which works on the Integral Formulation of the Maxwell Equations.
You are doing something very intelligent. You are simulating a device using two completely different numerical methods to see of the results match. Despite what anybody may tell you, they absolutely should match! When everything is correct, you may find some very subtle differences, but if you are getting completely different results that means something is wrong with one or both of your simulations. What you are doing is very good practice. Keep it up!!!
I suggest finding a known FSS from the literature to simulate. Try both your time-domain and frequency-domain solvers and set things up just like how you are trying to simulate your FSS. You can use the known case to root out what is wrong with your simulations. It may take some practice and duplicating several results from the literature. Just be confident that eventually the results from your two solvers should match pretty closely if you are setting up your simulations correctly.