Notice in two story capitals and in figures the top half is not the same as the bottom half. In other words if you divide a letter exactly in half while you create a font, the top half will appear too big visually. In order to balance the letters the center is slightly above the mathematical center and also top halves are drawn slightly narrower then bottom halves. Horizontal strokes in curved and straight letters are drawn thinner than vertical strokes so that horizontal doesn't appear too thick. Junctions where strokes meet are opened slightly so that the letter doesn't appear too thick at these junctions.
Curved strokes are thicker at their midsection than the vertical strokes to get an even appearance.
Having pointed these differences out to you, let me also say that these differences are very subtle and you probably will never notice them. But they help produce a more harmonies font. Now let's look at basic classifications of typefaces. There are many many type styles available today. IT will be hard to put them in categories.