HTML and HTML5 is the same markup language but the difference is that HTML5 has a consistent and defined error handling across browsers. What it means that you can write some code that is not absolutely correct for all browsers and HTML5 will have it corrected into a valid document.
HTML5 is trying to help browsers to display things more consistently and save money and time for browser developers.
Another cool thing about HTML5 it is attempting to make browsers more like a platform. tags, local storage, flash etc