The words do, doe, dough sound the same but have different meanings and spellings. Why do do, doe, dough sound the same even though they are completely different words?
The answer is simple: do, doe, dough are homophones of the English language.
To set or style (the hair).
To perform or execute: do one's assigned task; do a series of business deals.
To fulfill the requirements of: did my duty at all times.
To carry out; commit: a crime that had been done on purpose.
The female of a deer or related animal.
The female of various mammals, such as the hare, goat, or kangaroo.
A soft, thick mixture of dry ingredients, such as flour or meal, and liquid, such as water, that is kneaded, shaped, and baked, especially as bread or pastry.
A pasty mass similar to this mixture.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.