(") are quotation marks, we use them them by quoting someone for example, in a story it would say...
"I dont want to go!" said Bob.
(') is an apostorphe. You can use them in quotes for example
" 'I dont want to go!' said Bob."
Here I am quoting the the Bob statement.
The apostrophe can also be used in the ommison of letter for a word for example
~don't=do not
~won't
~wouldn't