I have recently been doing some researching on the problem described by OP for a similar question on SO. It seems that a bug in Firefox is causing the rendering of this so called "not-padding-but-looks-like-padding" on textarea elements.
Usually this extra padding is not really an issue, but it becomes an issue when you want to keep two elements the same width, and you care about getting its content to wrap the same way in both elements.
It seems to be impossible to get rid of this 1.5px wide padding on the textarea in Firefox, so if you want to ensure that the content wrapping inside a div in Firefox behaves exactly the same as the content wrapping inside a textarea in Firefox, the best approach seems to be to add an additional 1.5px of padding on the right and the left hand side inside the div, but only in Firefox. You can accomplish this by setting the following vendor specific prefixed CSS properties on your div:
The first ensures that the padding set on the div does not increase the width of the div, and the next two ensure that 1.5px of padding will be set on the right and the left hand side of the div.
This approach does not affect the rendering of the div's in any other browsers, it doesn't need to, as textarea's in other browsers don't render any extra padding. But it ensures that there are no content wrapping differences between div's and textarea's inside Firefox as long as they share the same font-family and font-size properties and so on.
Here's a jsFiddle for demonstration purposes.
If you only wanted to ensure that a textarea in Firefox has the same width and wrapping behaviour as a textarea in other browsers, you can set its box-sizing to border-box, add a padding on both sides of 5.5px and set -moz-padding-end and -moz-padding-start to 0px.
padding: 0 5.5px 0 5.5px;