Summary Ahead

~/.bash_profile ~/.bash_login, and ~/.profile are read by login shell in that order, but only the first one existing will be loaded by default.

~/.bashrc is loaded in non-login shell if it exsits.

Background

Bash was developed as a part of GNU project, and is now extensively distributed in the POSIX sytems. It loads a collection of startup files to help create an environment. ~/.profile, ~/.bash_profile and ~/.bashrc are the common ones located in the home directory.

What are the differences?

~/.bash_profile, ~/.bash_login, ~/.bash_logout and ~/.bashrc are specific to the Bash shell, while .profile is a generic config file read by many shells when their specific config files are missing.

When bash is a login shell, or invoked with --login, it firstly reads and executes commands from the file /etc/profile, if that file exists. Then, it looks for ~/.bash_profile ~/.bash_login, and .profile, in that order. It only reads the first one that is existing and readable.

When it is not a login shell, bash reads and executes commands from /etc/bash.bashrc and ~/.bashrc, if they exist.

Exiting

When a login shell exits, bash reads and executes commands from the file ~/.bash_logout, if it exists.

Options

The --noprofile and --norc may be used to start a login and non-login shell without loading profiles.

The --rcfile option will force bash to read and execute commands from a user specified file instead of /etc/bash.bashrc and ~/.bashrc.

Lazy Loading

For convenience, people usually load other profiles in one. For example, in .profile,

if [ -n "$BASH_VERSION" ]; then
    # include .bashrc if it exists
    if [ -f "$HOME/.bashrc" ]; then
        . "$HOME/.bashrc"
    fi
fi

References

Bash man page.