What's the difference between physically based lighting, physically based rendering and physically based materials? How they are different from deferred and forward rendering? And physically based rendering is used in films and deferred rendering is used in games?
Physically based rendering basically means that you strive to have realistic materials and lighting calculations. The way you do this can vary a bit (or a lot) depending on application, but the main idea is that no material can reflect more light back than hits it, and preferably you want to measure the Bidirectional reflectance distribution function (or BRDF) of the materials you use.
To get the best results you need to spend a lot of processing power to get the lighting just right, which means it is much more applicable for films, especially mixed actor/CGI films where the difference in lighting would be much more noticeable.
For games it is very easy to make a shader which glows without casting any light or that reflects three times the light that hits it, but since these are impossible materials in real life it won't look right if the rest of your scene is realistic looking (if you use cel/toon shaders or other non realistic things this wouldn't apply of course).
You can make a game strive for physically based rendering as well, with both forward and deferred rendering, the biggest hurdle is the lighting and shadows calculations. Using a BRDF shader is relatively easy, calculating the way the sunlight through a window lights up an otherwise dark room is much harder to get right in realtime.
For a much more in depth discussion on the subject, see The Physics of Light and Rendering | A Talk by John Carmack
Those terms are very imprecisely defined, and their definitions will vary from person to person, or from engine to engine.
There is a quick and easy introduction at this page, you may want to take a look at it.
I've only done games, so I can't tell you much about films. This being a game development Q/A, it is unlikely that you will find many people with experience in the film industry.
However, I hypothesize that for filmmaking, since a film does not need to be rendered in real time, you can use models and algorithms orders of magnitude slower that give much better results than what you can use for games.
For films you could also probably hand pick scenes and do manual postprocessing on them, or cheat a lot in the parts that are not visible to the spectator. In games you most likely won't be able to do that.
Apart from that, I assume gamemaking and filmmaking is very similar, in terms of the techniques used for rendering.
Regarding deferred and forward rendering, these terms loosely refer to the order in which rendering is performed, and cannot be compared with "physically based lighting".
To put it simply, there are lighting techniques that require deferred rendering, while others can be done with forward rendering. Some lighting techniques can be physically based or not (the definition varies according to the author).