The words peer, pier sound the same but have different meanings and spellings. Why do peer, pier sound the same even though they are completely different words?
The answer is simple: peer, pier are homophones of the English language.
To look intently, searchingly, or with difficulty. See Synonyms at gaze.
To be partially visible; show: The moon peered from behind dark clouds.
A person who has equal standing with another or others, as in rank, class, or age: children who are easily influenced by their peers.
A platform extending from a shore over water and supported by piles or pillars, used to secure, protect, and provide access to ships or boats.
Such a structure used predominantly for entertainment.
A supporting structure at the junction of connecting spans of a bridge.
Architecture Any of various vertical supporting structures, especially:
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.