Does direct tweet increases tweet count in my website tweet button?



I have tweet button in my blog post. If someone shares my blog page directly (without using tweet button in my blog post) my tweet count should increase. Please let me know if we can implement it n how.

For more information— here is query i received, for whom i am seeking solution
"I have seen widgets which show the Number of tweets even if someone shares the article on Twitter independently without clicking on Tweet button on the blog."



The count displayed by tweet buttons ( does include links tweeted directly (without using a tweet button).