The words plum, plumb sound the same but have different meanings and spellings. Why do plum, plumb sound the same even though they are completely different words?
The answer is simple: plum, plumb are homophones of the English language.
The fruit of such a tree.
Any of several shrubs or small trees of the genus Prunus, bearing smooth-skinned, fleshy, edible fruit with a single hard-shelled stone that encloses the seed.
The fruit of any of these trees.
Any of several trees bearing plumlike fruit.
A weight on the end of a line, used to determine water depth.
A weight on the end of a line, used especially by masons and carpenters to establish a true vertical.
In a vertical or perpendicular line.
Informal Directly; squarely: fell plumb in the middle of the puddle.
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.