The words right, rite, wright, write sound the same but have different meanings and spellings. Why do right, rite, wright, write sound the same even though they are completely different words?
The answer is simple: right, rite, wright, write are homophones of the English language.
Conforming with or conformable to justice, law, or morality: do the right thing and confess.
According to law, morality, or justice.
by rights In a just or proper manner; justly.
In accordance with fact, reason, or truth; correct: the right answer.
The prescribed or customary form for conducting a religious or other solemn ceremony: the rite of baptism.
A ceremonial act or series of acts: fertility rites.
The liturgy or practice of a branch of the Christian church.
One that constructs or repairs something. Often used in combination: a playwright; a shipwright.
To form (letters, words, or symbols) on a surface such as paper with an instrument such as a pen.
To spell: How do you write your name?
To form (letters or words) in cursive style.
To compose and set down, especially in literary or musical form: write a poem; write a prelude.
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.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").