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.
One that grates, as an implement with sharp-edged slits and perforations on which to grate foods.
One who or that which grates.
One who, or that which, grates; especially, an instrument or utensil with a rough, indented surface, for rubbing off small particles of any substance.
A <xref>tool</xref> with which one <xref>grates</xref>, especially cheese, to facilitate getting small particles or shreds off a solid lump.
Of, relating to, or being a city considered together with its populous suburbs.
<xref>comparative</xref> form of <xref>great</xref>: more <xref>great</xref>
Used in referring to a region or place together with the surrounding area; (of a city) <xref>metropolitan</xref>.
greater in size or importance or degree
Definitions from The American Heritage® Dictionary of the English Language, 5th Edition., from The Century Dictionary., from the GNU version of the Collaborative International Dictionary of English., from Wiktionary, Creative Commons Attribution/Share-Alike License., from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved. 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").