Basically Kernel is the interface between hardware (devices which are available in Computer) and Application software (like MS Office,Visual studio,..etc).If I come to tell what is OS then the answer could be the same .Hence kernel is the part & core of OS .The very sensitive task of OS like memory management,I/O management ,Process management are being taken care by kernel only.
So the ultimate difference is ,
Kernel is responsible for Hardware level interactions at some specific range. But the OS is like hardware level interaction with full scope of computer.
Kernel triggers SystemCalls to intimate os that this resource is available at this point of time.OS is responsible to handle that system calls in order to utilize the resource.*
Kernel——(SystemCall)——–> OS —–utilize the resource—–>