I think the issue you may be having is using terminology and a model from other operating systems and trying to apply them to CP/M.

CP/M evolved in the very early days of microcomputers as a single user system basically as a way for programs to be portable across multiple systems while doing console and file-based disk I/O via common calls. CP/M-2 was the most widely used and understanding it creates a foundation to understand CP/M-3 and MP/M. A lot has been written about it's internals but the basics are as follows in ascending memory order:

Location 0-0FFh - fixed functions / addresses and useage
TPA (Transient Program Area - memory for CCP-invoked .COM user programs from 100h-CCP
CCP (Console Command Processor) - Interpret console commands plus some resident commands - not used by transient programs and can be overlayed for additional memory space.
BDOS (Basic Disk Operating System) - Callable functions from CCP or user programs for console & disk I/O
BIOS (Basic I/O System) - Unique routines for each machine called by BDOS to perform lowest level I/O

As to the restarting of CCP: User (i.e. transient) programs normally finish in one of two ways:
1) If it has not overlayed the CCP then it can RETurn to CCP which invoked it.
2) A RST 0 or JP 0 which is an indirect jump to the BIOS warm start routine whose purpose is to reload the CCP (and often BDOS) then re-invoke the CCP.

Although I prefer not to use such analogies, "kernel" is most aptly the BDOS and the BIOS can be thought of as a collection of supporting I/O drivers. Note that since the BIOS is unique to each machine and implementation, there can be incompatibility when trying to use formatted media with data such as floppy disks on multiple systems.

CP/M-3 added banking to get around some of the memory limitations while MP/M added multi-user and multi-tasking support.