The words grater, greater sound the same but have different meanings and spellings. Why do grater, greater sound the same even though they are completely different words?
The answer is simple: grater, greater are homophones of the English language.
utensil with sharp perforations for shredding foods (as vegetables or cheese)
A <xref>tool</xref> with which one <xref>grates</xref>, especially cheese, to facilitate getting small particles or shreds off a solid lump.
One who, or that which, grates; especially, an instrument or utensil with a rough, indented surface, for rubbing off small particles of any substance.
One who or that which grates.
greater in size or importance or degree
Used in referring to a region or place together with the surrounding area; (of a city) <xref>metropolitan</xref>.
<xref>comparative</xref> form of <xref>great</xref>: more <xref>great</xref>
Of, relating to, or being a city considered together with its populous suburbs.
Definitions from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved., from Wiktionary, Creative Commons Attribution/Share-Alike License., from the GNU version of the Collaborative International Dictionary of English., from The Century Dictionary., from The American Heritage® Dictionary of the English Language, 5th Edition. and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.