Linux - Interactive, Non-interactive, login and non-login shells
A shell is the generic name for any program that gives you a text-interface to interact with the computer. You type a command and the output is shown on screen.
Many shells have scripting abilities: Put multiple commands in a script and the shell executes them as if they were typed from the keyboard. Most shells offer additional programming constructs that extend the scripting feature into a programming language.
On most Unix/Linux systems multiple shells are available: bash, csh, ksh, sh, tcsh, zsh just to name a few. They differ in the various options they give the user to manipulate the commands and in the complexity and capabilities of the scripting language.
Interactive: As the term implies: Interactive means that the commands are run with user-interaction from keyboard. E.g. the shell can prompt the user to enter input.
Non-interactive: the shell is probably run from an automated process so it can't assume if can request input or that someone will see the output. E.g Maybe it is best to write output to a log-file.
Login: Means that the shell is run as part of the login of the user to the system. Typically used to do any configuration that a user needs/wants to establish his work-environment.
Non-login: Any other shell run by the user after logging on, or which is run by any automated process which is not coupled to a logged in user.
For Bash, they work as follows. Read down the appropriate column. Executes A, then B, then C, etc. The B1, B2, B3 means it executes only the first of those files found.
+----------------+-----------+-----------+------+
| |Interactive|Interactive|Script|
| |login |non-login | |
+----------------+-----------+-----------+------+
|/etc/profile | A | | |
+----------------+-----------+-----------+------+
|/etc/bash.bashrc| | A | |
+----------------+-----------+-----------+------+
|~/.bashrc | | B | |
+----------------+-----------+-----------+------+
|~/.bash_profile | B1 | | |
+----------------+-----------+-----------+------+
|~/.bash_login | B2 | | |
+----------------+-----------+-----------+------+
|~/.profile | B3 | | |
+----------------+-----------+-----------+------+
|BASH_ENV | | | A |
+----------------+-----------+-----------+------+
| | | | |
+----------------+-----------+-----------+------+
| | | | |
+----------------+-----------+-----------+------+
|~/.bash_logout | C | | |
+----------------+-----------+-----------+------+
In more detail is this excellent flowchart from http://www.solipsys.co.uk/new/BashInitialisationFiles.html :
