There is a big difference between using relax or minimize. One reason is that when you use Relax(), it turns off various commands (temperature, electrical current, time-dependent magnetic fields), leading to the illusion that they are working during micromagnetic simulation, so knowing in detail the appearance of each command is important for the result and final interpretation of your simulated data.
Relax() tries to evolve the magnetization as closely as possible to the minimum energy state. This function assumes all excitations have been turned off (temperature, electrical current, time-dependent magnetic fields). During relax precession is disabled and the time t does not increase. There is no need to set high damping. In general it is difficult to be sure the minimum energy state has been truly reached. Hence, relax may occasionally return after the energy has reached a local minimum, a saddle point, or a rather flat valley in the energy landscape.
Minimize() is like Relax, but uses the conjugate gradient method to find the energy minimum. It is usually much faster than Relax, but is a bit less robust against divergence. E.g., a random starting configuration can be Relaxed, but may fail with Minimize. Minimize is very well suited for hysteresis calculations, where we are never far away from the ground state.