The kernel has two different debugger front ends (kdb and kgdb) which interface to the debug core. It is possible to use either of the debugger front ends and dynamically transition between them if you configure the kernel properly at compile and runtime.
Kdb is simplistic shell-style interface which you can use on a system console with a keyboard or serial console. You can use it to inspect memory, registers, process lists, dmesg, and even set breakpoints to stop in a certain location. Kdb is not a source level debugger, although you can set breakpoints and execute some basic kernel run control. Kdb is mainly aimed at doing some analysis to aid in development or diagnosing kernel problems. You can access some symbols by name in kernel built-ins or in kernel modules if the code was built with CONFIG_KALLSYMS.
Kgdb is intended to be used as a source level debugger for the Linux kernel. It is used along with gdb to debug a Linux kernel. The expectation is that gdb can be used to "break in" to the kernel to inspect memory, variables and look through call stack information similar to the way an application developer would use gdb to debug an application. It is possible to place breakpoints in kernel code and perform some limited execution stepping.
Two machines are required for using kgdb. One of these machines is a development machine and the other is the target machine. The kernel to be debugged runs on the target machine. The development machine runs an instance of gdb against the vmlinux file which contains the symbols (not a boot image such as bzImage, zImage, uImage...). In gdb the developer specifies the connection parameters and connects to kgdb. The type of connection a developer makes with gdb depends on the availability of kgdb I/O modules compiled as built-ins or loadable kernel modules in the test machine's kernel.