OK, actually this is correct and what the difference between the two files is (profile is loaded by a login shell, bashrc is loaded by an interactive shell), but can you tell me the real difference between ~/.bash_profile and ~/.profile?
The real answer is, read the entire man page to understand.
From the page .bashrc runs in every shell, so long as it is an interactive shell. Bash can be interactive according to a complex system of connected variables, including $PS1, $-, and the arguments passed into bash itself. I found all of this described fully in the Invocation section of the man page, section on interactive shells.
However, profile is loaded when the shell is a login shell. Which profile? Also from Invocation, continuing on from an explanation of when .bashrc is loaded:
> 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.
So, .bash_profile may or may not be loaded, and .profile being loaded or not loaded depends on the existence of those other two files in order.
Your response was lazy but on point. This is the darkest of man page magic, and nobody who hasn't read the manual will know the answer in complete detail. Everyone who has spent any real time in a shell has learned part of this answer.
The reason for that is that .profile was also read by login Bourne and Korne shells, with which bash is supposed to be backward compatible.
So if you only have a .profile, it makes sense to source that. If you have one of the bash-specific ones, then it's up to you whether you want to `source` the common .profile one or not.
The real fun comes when you want to run commands in every shell, whether interactive or not. For example, aliases that you want available when you use shell escapes like ! in vi.
The only way to do that is to have the file's path explicitly in $ENV, or $BASH_ENV of course...
