.bash_profile, .bash_login, .bashrc, and .profile all do pretty much the same thing: set up and definefunctions, variables, and the sorts.
The main difference is that .bashrc is called at the opening of a non-login but interactive window, and .bash_profile and the others are called for a login shell. Many people have their .bash_profile or similar call .bashrc anyway.
.profile vs .bash_profile (and .bash_login)
.profile is read by most shells on startup, including bash. However, .bash_profile is used for configurationsspecific to bash. For general initialization code, put it in .profile. If it’s specific to bash, use .bash_profile.
.profile isn’t actually designed for bash specifically, .bash_profile is though instead. (.profile is for Bourne and other similar shells, which bash is based off) Bash will fall back to .profile if .bash_profile isn’t found.
.bash_login is a fallback for .bash_profile, if it isn’t found. Generally best to use .bash_profile or .profile instead