Commands are things that run when you type them at the command prompt. Some are built into the shell, some are external executables, some are both. The technical terms for this are "built in" and "external". There is no "true" command vs false command (but there are commands that can return true or false).
"utility" is has no particular technical meaning in unix and doesn't distinguish anything special. Any such distinction is in the documentation only and does not affect operating system function or operation, or distinguish between different types of executables or sources of executables.
Since there is no technical meaning for "utility" different documentation defines it differently and leaves some abiguity.