Homophones
'Their', 'there' and 'they're' sound identical
Homophones are words that sound the same but differ in spelling and meaning. English has thousands of them because it borrowed spellings from many languages.
More in Homophones
'Bare' and 'bear' trip up writers
Bare means uncovered, bear means to carry or the animal. Spellcheckers ignore the difference because both are real words.
'Complement' and 'compliment' differ by a letter
A complement completes something, a compliment praises it. Both trace back to Latin complere, to fill up.
'Peace' and 'piece' come from one root
Both descend from Latin pax, since a piece was originally a portion settled by agreement.