Difference between white sugar, brown sugar and red sugar
The white sugar you refer to as "normal" sugar is mostly pure sucrose, which forms translucent whitish crystals.

White sugar doesn't start out white --- it's actually refined from a plant extract (primarily from sugarcane) that is a mixture of sucrose, glucose, fructose, and some minerals including calcium, iron, and magnesium. The unrefined extract is "raw" sugar, and these minerals give it a brown color.

Brown sugars are partially-refined sugars which still have some of the other components besides sucrose. When it's fully refined, the appearance is white.

When we refine the raw sugar, the remainder is referred to as molasses -- a dense, dark brown syrupy mixture of sucrose, glucose, fructose, and some minerals which give it the signature dark brown color.

Red sugarcane doesn't produce red sugar as @LDC3 stated. "Red sugar" is actually refined sugar with a red pigment added to it... unless you're talking about what the Chinese refer to as "red sugar" -- which is just their name for brown sugar!