The words peaking, peeking sound the same but have different meanings and spellings. Why do peaking, peeking sound the same even though they are completely different words?
The answer is simple: peaking, peeking are homophones of the English language.
Present participle of peak.
To glance quickly.
To look or peer furtively, as from a place of concealment.
To be only partially visible, as if peering or emerging from hiding: Tiny crocuses peeked through the snow.
A brief or furtive look.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, 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").