What are Bash startup files?

gnu.org/software/bash/manual/bash.html#Bash-Startup-Files

1. 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.

gnu.org/software/bash/manual/bash.html#Invoked-as-an-interactive-login-shell_002c-or-with-_002d_002dlogin

2. Invoked as an interactive non-login shell

When an interactive shell that is not a login shell is started, Bash reads and executes commands from ~/.bashrc, if that file exists.
This may be inhibited by using the --norc option.
The --rcfile file option will force Bash to read and execute commands from file instead of ~/.bashrc.

So, typically, your ~/.bash_profile contains the line

if [ -f ~/.bashrc ]; then . ~/.bashrc; fi

after (or before) any login-specific initializations.

gnu.org/software/bash/manual/bash.html#Invoked-as-an-interactive-non_002dlogin-shell

3. Invoked non-interactively

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.

gnu.org/software/bash/manual/bash.html#Invoked-non_002dinteractively

4. Invoked with name sh

If Bash is invoked with the name sh, it tries to mimic the startup behavior of historical versions of sh as closely as possible, while conforming to the POSIX standard as well.

When invoked as an interactive login shell, or as a non-interactive shell with the --login option, it first attempts to read and execute commands from /etc/profile and ~/.profile, in that order.
The --noprofile option may be used to inhibit this behavior.
When invoked as an interactive shell with the name sh, Bash looks for the variable ENV, expands its value if it is defined, and uses the expanded value as the name of a file to read and execute.
Since a shell invoked as sh does not attempt to read and execute commands from any other startup files, the --rcfile option has no effect.
A non-interactive shell invoked with the name sh does not attempt to read any other startup files.

When invoked as sh, Bash enters POSIX mode after the startup files are read.

gnu.org/software/bash/manual/bash.html#Invoked-with-name-sh