Story or development art.
Exploratory- exploration of idea at the start of a project to define the look or think of what might be possible. Can be rougher of more varied in the search for solutions while trying to nail down what or who the characters are
Can be used to inspire
Mood pieces that match environment or character with a the story, or show atmosphere or drama to sell the project..
Thumbnails
Thumbnails are small quick sketches which convey the idea of the character of creature. Thumbnails are great because normally they have a lot of life- and overall gesture to their action- because of the scale you normally do them. Sometimes theres a really beauty of line or expression you get thats very hard to get in a fully realised drawing. The down side is they suggest so much but nothing is too worked out or 'nailed down'(I think the saying is - they promise the world but deliver nothing)- sometimes it's hard to draw through the smog of suggestion you created to capture the true lines you were after. I f you are wanting to refine your thumbnails using pencil and paper you could use a lightbox, or better yet a photocopier to blow up the thumbnails bigger and then trace through and clean them up. On computer though you'd just add a new layer in photoshop and draw over the top(and maybe reduce the opacity of your thumbnail layer so you can see better. I often do my roughs or thumbnails on computer in a cloudy hazy brush and then sharpen it and darken the lines and add shadows(or I just use a sharp line like a pencil and then add shadows etc.
Silhouettes,
Roughs in line or greyscale, or in colour if you are tricky..
The great thing about doing roughs or putting ideas down in pencil or pen on paper is that it forces you to think more about what you are drawing or what you want- more at least than a computer. There are a lot of techniques you see on computer where they use a semi random -kind of ink blot style of creativity. People will create an odd and interesting shape with funny or random or custom brush strokes and then go in and try to make sense of the design or try to refine it. the good thing about this is you can get some great interesting shapes and wacky spun out looking designs quickly-except they probably make no sense in a design sense- or its a struggle to make them resolve into a 3d shape. Why do they need to be a realisable 3d shape - because for a game or film- someone needs to make the design into a 3d shape. I f the drawing is to stay a drawing then it doesn't matter and probably the mood or impression is the key thing you are after.
When you are drawing sometimes changing your medium canchange the way you approach drawing and give you different shapes and designs- for free.
When you cleaning up roughs the sort of things you might do is introduce proper perspective and correct anything that doesn't follow the perspective of the view. You might lay a basic grid over or under the drawing- or even just some "eyeballed" converging perspective lines and use that to make all of the drawing 'agree'. Particularly tricky things like ellipses and concentric ellipse shapes are cleaned up either with templates, or with an ellipse tool in photoshop, or by aligning a quick 3d model in photoshop or a 3d package and tracing over that. Ellipses are the shapes circles and circular cross section forms take on when seen in perspective(sort of like a squashed circle). Ellipses are located in perspective drawings by placing them in a square the same size, and oriented by lining up their minor axis with a perspective line to the horizon(major axis is a little offset from the centre of the perspective square the ellipse sits in).
When you are cleaning up or fixing drawings (or even when you do them in the first place) its useful to flip the paper (or your computer image)and look at the reverse image. Adding in a centre line(like a moulded 'part' line) to the character or creature you are drawing can help with the placement of symmetrical features and can help when you are drawing curved shapes. (Particularly for eyes and determining the visibility of 'far' shoulders)
In the long term its a good thing to keep a sketchbook of roughs or at least ideas book. Even doing a few thumbnails or roughs on paper can be good preparation before hitting the computer- again because it focusses you on what you want to achieve. Even animator who work on computer will do a bunch of small rough images of the poses and attitudes, and shapes they want to hit before starting on the computer proper.
Refining a design.
Variations might be developed for details such as colouration texture, or variations of accessories.
Sometimes when the basis of the character or creature is defined a common or duplicated base drawing is used and the different options or variations painted on top to save drawing the character again- this is where computers are handy. This make things quicker but has the danger of producing variations for the sake of variations.
A base drawing of a generic character or a standardised human or game character is used when creating clothing or amour variations for customisable characters. Sometimes in these cases a bases predrawn stock human figure is the starting point,- sometimes in a game its the rendered stock human model that you then "decorate".
Different States.
If a character has different states in a game or through a story these will need to be visualised like damaged or powered up states. The more extreme example is the case of a boss type creature which might change or present in a number of way in a fights.