| Are they drawn on paper with pen and pencil and then scanned into digital format? |
No. Concept art for a game might be done on paper, and you might be able to find one or two games that have done it this way for stylistic reasons, but in general it is impossibly difficult to digitize a hand-drawn drawing into something that is useful in a game.
| Are they made in Adobe Photoshop pixel by pixel taking huge amount of time and effort? |
An image editor is an essential part of graphics design. Depending on the game's art style and the artist, they may use a digital pen type device for drawing parts of the image in combination with digital manipulation of the image.
| So, what's the difference between these two types of graphics? |
The only definition for "NFS" that I was able to come up with was "Need For Speed", so I'll assume that basically you're asking about the difference between a 2d platformer and a 3d game.
Many 2d platformers, particularly older ones, use "sprites" for graphics. Basically, these are independent images that are stitched together to form the overall scene. For example, in a top-down style game you might have four sprites of your player character - one facing north, one facing south, one facing east, one facing west. The game engine would choose which to display and where to display it based on the state of the game. In this way you end up with a vast number of small 2d images that would be created using an image editor.
You can also make peusdo-3d graphics using this method, which often use an isometric viewpoint. For example, the older Sim City games.
3d games are completely different and obviously far more complicated. Generally you start by defining the three dimensional shape of an object using modeling software similar to engineering CAD software. Next you create an image called a texture that will be wrapped around that shape and gives it the appropriate colors. That part might be done using a standard image editor. There are various other "images" that you might construct as well, bump/depth maps or light maps that help tell the game engine how to render the object's lighting. These are often gray-scale images where white is one extreme and black is the other (depending on what the image represents).
I'm not very familiar with animation in 3d games, but I believe that it's usually done by defining "joints" in the model and then using animation algorithms to interpolate how the shape would transition from one position to another.
The rendering of 3d graphics is far more complicated than actually making them. It's best to leave that to a pre-made engine unless you have degrees in both mathematics and computer science.
| So, please tell me how are graphics made? What are the steps towards making graphics for a game? |
And, say if I have graphics, how do i program them? Like do I keep a record of relative position of the hand of an actor in the game and keep checking if his hand is touching the wall (just for example)
These questions don't really have simple answers. How you make graphics depends on what kind of graphics you are making, and even then there are many different ways to do it. Likewise, programming the graphics depends on what sort of graphics you are programming. You should probably start by just making a game that displays flat images on the screen. Then find a third party engine that will dictate to you how your graphics need to be constructed and programmed.