Such a resident monitor is frequently called a debugger, boot loader, command-line interface (CLI), etc.
The original meaning of serial-accessed or terminal-accessed resident monitor is not frequently used, although the functionality remained the same, and was augmented.
Also, code can be downloaded and uploaded from various sources, and some advanced monitors support a range of network protocols to do so as well as formatting and reading FAT and other filesystems, typically from flash memory on USB or CFcard buses.
For embedded processors, many in-circuit debuggers with software-only mode use resident monitor concepts and functions that are frequently accessed by a GUI IDE.
In many cases resident monitors can be a step up from printf debugging and are very helpful when developing on a budget that does not allow a proper hardware in-circuit debugger (ICD) to be used.