Difference between Write-Host and Write-Output in PowerShell

I have been using PowerShell for quite a few years and I have never been very clear about their differences so I decided to research it further.

As it turns out, these 2 articles do a very good job of explaining the differences between these 2 very similar-looking commands:

http://windowsitpro.com/windows/write-output-or-write-host-powershell

http://www.jsnover.com/blog/2013/12/07/write-host-considered-harmful/