In the simulation, you will set how long one step is. For example, in a simulation of metals, one step is usually set as 1fs. 100000 steps is 100ps. After you get the time, it is easy to obtain the cooling rates.
I don't know the full context of the above sentence, but I understand that you might have difficulty understanding the term "relaxed". From my experience, this actually means relieving the pressure arising in the system. That is using NPT ensemble at 0 bar pressure.
You can control the cooling rate by setting Tstart and Tstop as desired and set the duration of the run according to the desired cooling rate in units of K/time
In molecular dynamics the system evolves in very short time steps, typically 1 or 2 femtoseconds. If, for example, the step is 2 fs, then your simulation runs over 0.2 ns to equilibrate, followed by 0.8 ns to collect the averages.
You control the cooling rate in a simulation since you can set the "${T_start}" and "${T_stop}" on your thermostat while using either a "fix npt" or "fix nvt" for a desired number of "${steps}". You can obtain the total time taken for the run by multiplying the steps with the timestep that you're using and then the cooling rate that you are imposing (not calculating from the MD trajectory), since C_rate = (T_stop - T_end)/(steps*timestep).
100,000 steps and 400,000 steps both mean the number of iterations in a course of simulations.
Like what Y. Zhu said, the simulation time should be the product of the given time step size (delta t) and the number of iterations. For instance, if you set the time step size to be 0.25 fs, and you go through 100,000 steps and 400,000 steps for course A and course B, then the simulation times for course A and B are 25 ps and 100 ps.
As far as I understand, 100,000 steps would be the number of iterations in a minimization course, typically keeping the temperature at 0 K or at a low value, for the purpose of obtaining an optimized geometry that excludes the temperature effect. 400,000 steps would be the number of iterations in an equilibration course, where one should always apply a thermostat to the simulation. As such, you are relaxing your geometry with molecular dynamics (MD), where temperature plays a crucial role. The reason of doing geometry minimization ahead of MD is that we want all atoms to have a reasonable initial velocity distribution (Maxwell-Boltzmann) corresponding to the designated temperature for the MD step(s).
I want to leave introductory remarks to the more detailed and specific comments above.
General
In MD simulation, the potential of interatomic or intermolecular interaction is used (a function of potential energy in particle coordinates). At each step, the forces of interatomic interaction are calculated for all particles of the system. The integration is used to get the particle velocities that they got in 1 step, i.e. the default is one femtosecond. At each step, the coordinates, velocities and forces of the particles change. By default, LAMMPS uses the Verlet integrator program to calculate particle velocities.
Private
In order to warm up your system, you must first apply the thermostat, that is, these are the fix nvt commands or, for example, fix npt. As you understand, nvt means constant temperature, number of particles, volume, and npt is constant pressure, but not constant volume - this is also an additional barostat, that is, an algorithm that sets constant pressure. Then you need to make sure that the system really has the right temperature (!) This, in turn, can be done using the thermo_style custom step temp commands and the thermo command (after how many steps to display), these commands display data on the screen. Don't forget to set the run command as it runs the molecular dynamics simulation. After heating the system, it is necessary to keep it at the same temperature for some time in order to reach equilibrium. At this point, I recommend writing a dump file. Next, you need to use the fix npt (nvt) command to change the temperature, that is, to cool. And don't forget to put the run command stage, that is, during heating, exposure and cooling..
Note: We have two temperatures. There is a temperature that we set (it's just a goal). There is a system temperature (it is set during simulation). The second temperature is very important for us. There will be fluctuations, despite the fact that this is a thermostat.