1) Use Firefox
2) Install Firebug plugin
3) Inspect the table and the elements in it..to see the associated css that controls how the table elements are displayed.
You will see the first example has almost no styling defined...so the browser uses its own...ie it may look slightly different in different browsers.
The second example has stying defined...including no borders on td elements. You can temporarily disable bits of the css in Firebug and you will see how it will end up looking like the first example.

Since actually disabling everything will probably bugger up other things on your site, give the table a unique id and style it as necessary.