Some controversy exists about just what is "configurable" and what is "extensible" for soft, synthesizable microprocessor cores. Classic definitions that seem to stand are:
Configurable: adding or removing already defined resources to or from the core. These could include instructions, general registers, and condition codes.
Extensible: adding something new to the core. These could be instructions, special registers/interfaces, condition codes (with special logic), functional blocks, and so forth. Basically, they all involve new, just-now-defined logic.