The words acclamation, acclimation sound the same but have different meanings and spellings. Why do acclamation, acclimation sound the same even though they are completely different words?
The answer is simple: acclamation, acclimation are homophones of the English language.
A shout or salute of enthusiastic approval.
An oral vote, especially an enthusiastic vote of approval taken without formal ballot: a motion passed by acclamation.
The process of acclimating or of becoming acclimated.
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").