restart and shutdown

Yes, there is a difference. During a working session various files loaded into memory "as needed". Windows will arbitrarily keep some of these loaded because it determines that they will be needed again and again. So rather than reload them over and over, windows simply doesn't unload them. When you choose restart, Windows restarts the OS but does not necessarily unload everything from memory. When you choose shutdown, everything is cleared from memory and only the OS and startup items are loaded on reboot. So A restart only restart the OS and a shutdown shuts everything off including Hard Disk Drive HDD, RAM, Network card,...I hope that was what you are looking for.

I've read long back, that when we manually restart the machine Memory test is performed (called Cold Boot) whereas if we restart it through OS no memory test is performed (called Warm Boot) But that was for the old versions. So, I am not sure this is still correct.

It is the operating system, that runs the computer for you. It acts as an interface between the user and the machine. "Shut Down" means turning off the computer. When this command is selected, the Operating System first finishes or kills all the running processes, save any unsaved data or changes made and then switches off the computer. "Restart" means first to shut down the machine and then put it on again. Putting on the computer includes booting the computer, loading the OS. Several processes are created by the OS in this event, which are needed for the computer to run properly.