What are the differences between a login shell and interactive shell?

An interactive shell is one started without non-option arguments, unless -s is specified, without specifying the -c option, and whose input and error output are both connected to terminals (as determined by isatty(3)), or one started with the -i option.

An interactive shell generally reads from and writes to a user’s terminal.

[gnu bash manual]

A login shell is a shell where you login. You can recognize a login shell from a ps -f listing, it will have a hyphen at the start of the program name, for example:

root      3561  3553  0 09:38 pts/0    00:00:00 -bash
qa        7327  3432  0 10:46 pts/1    00:00:00 -bash

An interactive shell is one which reads commands from it's standard-input, usually a terminal.

For example, if you login to bash using an xterm or terminal emulator like putty, then the session is both a login shell and an interactive one. If you then type bash then you enter an interactive shell, but it is not a login shell.

If a shell script (a file containing shell commands) is run, then it is neither a login shell nor an interactive one.

Start-up files are highly tailorable in bash:

When a login bash shell is invoked, then /etc/profile is sourced (executed in the current environment). After that, three files are checked for existence. The checks for these files are done in this order:

if /etc/profile exists, source (run) it
if ~/.bash_profile exists, source (run) it
if ~/.bash_login exists, source (run) it
if ~/.profile exists, source (run) it

Once a match is found, the other files are ignored, even if they exist. The /etc/bashrc file might be used by both the ~/.bash_profile and the ~/.bashrc files. That would mean that the /etc/bashrc file is sourced on all interactive invocations of bash, whether it is a login or non-login shell.

So, the .bashrc file is also run every time you request a new interactive shell. This does not include a shell script. Normally variables, aliases or functions are placed in this file.

Bash shell scripts read a different file if suitably instructed. If the user defines (usually in their own .bash_profile) a variable BASH_ENV which contains a filename, scripts will read this. If this variable is not set (and exported) then bash scripts will not read any startup files.

Since you probably know what a "shell" is and are using it your question only targets the difference between login shell and everything else...

A login shell only differs from any other shell by the fact that one or more initial setup scripts (resources) are loaded on startup, typically named with "profile" in their name. in there basic settings are defined that are derived to subsequently opened shells (so they only need to be defined once).