Why does the Emacs ansi-term and Emacs shell PS1 prompt not match my system PS1?

Question

I'm running Mac OS 10.10.3; Emacs is complied and installed via Homebrew; I run it as a GUI application and it reports

This is GNU Emacs 24.4.1 (x86_64-apple-darwin14.1.0, NS apple-appkit-1344.72)
 of 2015-03-23 on boomer

Inside of Emacs shell or Emacs ansi-term, my prompt looks like this:

bash-4.3$ echo $PS1
\s-\v\$

But inside of Terminal.app, my prompt looks like this:

boomer:~ dgrady$ echo $PS1
\h:\W \u\$

The value of PS1 that Terminal.app sees comes from the system-wide /etc/bashrc file, which reads

# System-wide .bashrc file for interactive bash(1) shells.
if [ -z "$PS1" ]; then
   return
fi

PS1='\h:\W \u\$ '
# Make bash check its window size after a process completes
shopt -s checkwinsize
# Tell the terminal about the working directory at each prompt.
if [ "$TERM_PROGRAM" == "Apple_Terminal" ] && [ -z "$INSIDE_EMACS" ]; then
    update_terminal_cwd() {
        # Identify the directory using a "file:" scheme URL,
        # including the host name to disambiguate local vs.
        # remote connections. Percent-escape spaces.
        local SEARCH=' '
        local REPLACE='%20'
        local PWD_URL="file://$HOSTNAME${PWD//$SEARCH/$REPLACE}"
        printf '\e]7;%s\a' "$PWD_URL"
    }
    PROMPT_COMMAND="update_terminal_cwd; $PROMPT_COMMAND"
fi

Why do Bash shells I start from within Emacs not see the same value of PS1?

Answer 1

Terminal.app starts an interactive login shell, while Emacs starts interactive non-login shells. The Bash manual's section on startup files explains that for login shells, Bash will first source /etc/profile (and on Mac OS this file instructs Bash to source /etc/bashrc, which sets PS1) and then goes on to look for user-specific config files. Interactive non-login shells look only for user-specific config files.

One way to check that this is the case: in Emacs,

bash-4.3$ echo $0
/usr/local/bin/bash

while in Terminal.app,

boomer:~ dgrady$ echo $0
-bash

Related: https://unix.stackexchange.com/questions/119627/why-are-interactive-shells-on-osx-login-shells-by-default