Web Browsers and the DOM
The W3C DOM standard gives web browsers a basis for how the DOM should be implemented. Web browsers implement this standard in different ways. All web browsers use their own implementation of the DOM, because they each extend the W3C DOM standard in their own way.
Browsers currently conform to this standard more closely than in the past. They continue to get closer to a standerdized DOM. The end result is less work for web developers.
But since each browser still has its own version of the DOM, your webpage must be cross-browser tested for compatibility. If there is a difference, you will have to program your webpage one way for one web browser and a different way for another web browser.