The words place, plaice sound the same but have different meanings and spellings. Why do place, plaice sound the same even though they are completely different words?
The answer is simple: place, plaice are homophones of the English language.
An area with definite or indefinite boundaries; a portion of space.
Room or space, especially adequate space: There is place for everyone at the back of the room.
The particular portion of space occupied by or allocated to a person or thing.
A building or an area set aside for a specified purpose: a place of worship.
A large edible marine flatfish (Pleuronectes platessa) of western European waters.
Any of various flatfishes, such as Hippoglossoides platessoides of North American Atlantic waters, related to the plaice.
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").