Every Operating System (OS) has 2 parts. The kernel and the tools to manage the box. For example, Windows, is an OS, Linux is just a Kernel, GNU/Linux is a OS basically.
The kernel has several layers, for example, I/O, memory, scheduler, etc. Each part of the kernel, in the man-in-the-middle between the hardware and request to the hardware. So the kernel, will be catching any request to the hardware and call system functions to take care of that request. On the other side you have a set of tools that is the interface between the human being and the kernel. For example, when you login to the NX-OS CLI, that is called the shell. The shell translates the commands you run, makes a request to the device in question, (could be memory, external or internal flash, etc) and performs the request. In a switch, call it Nexus, Catalyst, MDS, you only have the shell to interact with the hardware. In a Windows, GNU/LINUX, Apple or android system, you have a set of graphic tools to do so much other things that just writing cryptic commands in the CLI. You tell that graphic tool to do something, that request is passed to the kernel, the kernel takes that request a do what needs to be done to complete it successfully.
That is a general idea of OS terminology and funtionality. Now, related to NX-OS, the kickstart image is the Kernel, and the system image is the set of tools and programs that run on top of that kernel. The NX-OS is based on a Linux kernel. So if you see both the start up of a Nexus or a GNU/Linux System, you will see that they are very similar.
THe kernel when it starts, will do the POST, check hardware and some other things. After the kernel says, "Hey, we are ok to go, the system image starts loading all the programs that need to start as configured.
