The words currant, current sound the same but have different meanings and spellings. Why do currant, current sound the same even though they are completely different words?
The answer is simple: currant, current are homophones of the English language.
Any of various deciduous, spineless shrubs of the genus Ribes, native chiefly to the Northern Hemisphere and having flowers in racemes and edible, variously colored berries.
The fruits of any of these plants, used for jams, jellies, desserts, or beverages.
A small seedless raisin of the Mediterranean region, used chiefly in baking.
Any of several other plants or their fruit.
Belonging to the present time: current events; current leaders.
Being in progress now: current negotiations.
Passing from one to another; circulating: current bills and coins.
Prevalent, especially at the present time: current fashions. See Synonyms at prevailing.
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").