From Bash Manual
Invoked as an interactive login shell, or with --login
When Bash is invoked as an interactive login shell, or as a non-interactive shell with the --login option, it first reads and executes commands from the file /etc/profile, if that file exists. After reading that file, it looks for ~/.bash_profile, ~/.bash_login, and ~/.profile, in that order, and reads and executes commands from the first one that exists and is readable. The --noprofile option may be used when the shell is started to inhibit this behavior.
When an interactive login shell exits, or a non-interactive login shell executes the exit builtin command, Bash reads and executes commands from the file ~/.bash_logout, if it exists.
Invoked as an interactive non-login shell
When Bash is started non-interactively, to run a shell script, for example, it looks for the variable BASH_ENV in the environment, expands its value if it appears there, and uses the expanded value as the name of a file to read and execute. Bash behaves as if the following command were executed:
if [ -n "$BASH_ENV" ]; then . "$BASH_ENV"; fi
but the value of the PATH variable is not used to search for the filename.
As noted above, if a non-interactive shell is invoked with the --login option, Bash attempts to read and execute commands from the login shell startup files.
Which case does a noninteractive login shell belong to, the first case, or the third case?
The first case "Invoked as an interactive login shell, or with --login" contains the scenario of "non-interactive shell with the --login option", so I deduce that
the first case is for login shells regardless of being interactive or noninteractive, and
the third case is for noninteractive nonlogin shells.
Am I correct?