16 bit applications are those written to work on 16 bit processors - the same with the other sizes. This is further complicated by the design of the OS and the processors that it's intended to work with.
As computing grew more sophisticated, the amount of "bits" that each processor was able to process was increased to 32 bits. At that time there was a lot of issues with the ability to run 16 bit applications on 32 bit processors - until someone came up with the great idea to run the 16 bit program in a separate process (you can identify these in Task Manager by looking for the indented wowexec.exe and the ntdvm.exe processes (which indicate that it's running in a virtual DOS machine). http://www.microsoft.com/windowsxp/using/s.../spot16bit.mspx
Using 32 bit applications on 64 bit processors is much easier because software design has grown more sophisticated over the years. It's even possible to run a 64 bit OS on some (but not all) 32 bit processors. The 32 bit processor must have the ability to emulate a 64 bit processor.
Here's a Wikipedia entry that may help: http://en.wikipedia.org/wiki/16-bit_application
Kernel Mode Drivers are a bit more complicated and I don't fully understand it. But, it seems that it's a framework that allows drivers more control over their interaction with the CPU and OS - and because of this it's much more powerful (and, if poorly designed, more able to cause crashes). http://en.wikipedia.org/wiki/Kernel_Mode_Driver_Framework
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