The words inflection, inflexion sound the same but have different meanings and spellings. Why do inflection, inflexion sound the same even though they are completely different words?
The answer is simple: inflection, inflexion are homophones of the English language.
The act of inflecting or the state of being inflected.
Alteration in pitch or tone of the voice.
Grammar An alteration of the form of a word by the addition of an affix, as in English dogs from dog, or by changing the form of a base, as in English spoke from speak, that indicates grammatical features such as number, person, mood, or tense.
Grammar An affix indicating such a grammatical feature, as the -s in the English third person singular verb form speaks.
Chiefly British Variant of inflection.
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").