In another question posted today (03 April, 2016) user @Celeritas posted an almost identical question. The last answer to this question was posted almost 4½ years ago, so I believe an update is warranted.
Back in 2011 most HDDs parked their heads in the so-called landing zone. Today most HDDs park their heads completely off the drive (I've take enough apart to know this), so there is little difference between shutting down a HDD via a cold boot and a warm boot, as the heads in today's HDDs never contact the disks' surfaces.
I can't enumerate all the difference between a cold and warm boot, but a couple of big ones are the system and graphics RAM. Unless the graphics driver is specifically designed to do so, its RAM is not cleared during a warm boot. Whatever was there before the reboot will be there after the reboot, unless the video RAM gets overwritten during the reboot, which is probably 99.99% of the time, but that .01% can cause endless headaches. (On another machine I used to see bits and pieces of whatever was in my graphics RAM during a warm boot after the machine had shut down.) This can also be true of system RAM. At work before I retired, if we had problems with our servers (multiple app and database servers) and needed to restart them, we often could not clear the trouble without shutting down the machine for at least thirty seconds or more.
So if you're having problems with a computer that seems to be RAM related, the best advice is to shut down the computer for at least twenty, if not thirty, seconds and then start.
Said question was deleted in favour of this one. – Celeritas – 2016-04-04T02:09:41.710