Image width tag is less than the image pixel width – why?

640px is the content size set in your functions.php. Here is an example of the content width set in the bundled theme twentyfourteen in twentyfourteen/functions.php#L28

if ( ! isset( $content_width ) ) {
    $content_width = 474;
}

In this example, the image size will be 474 px.

The content size will be the size used when images are inserted as attachments in the content when creating posts

EDIT

From the comments from the OP, to remove this restrictions, have a look at the 2 following posts

• What is a good alternative to using $content_width for image optimization?

• WHY THE $CONTENT_WIDTH WORDPRESS SETTING HURTS OPTIMIZATION.