There are no directories, but "user areas" numbered from 0 to 15, so different users can have different files on the same disk. User areas are selected with the USER command. However, most people used user areas as poor-man's directories.
There is no COPY command. Copying files (and much more) is done with a program named PIP (peripheral interchange program). For instance,
PIP B:=A:*.COM[E]
would copy all files of the type COM from drive A: to drive B: and echo the file names.What was great about CP/M was that it allowed programs to run on different computers, as long as they were 8080- or Z80-based. It was a thin, but very effective abstraction layer between the hardware and a program.
MSDOS, which was originally based on CP/M, was a step back, really, because everybody tried to program the hardware directly instead of going through the proper interfaces.