<script> is HTML 5.

<script type='text/javascript'> is HTML 4.x (and XHTML 1.x).

<script language="javascript"> is HTML 3.2.

Is it different for different webservers?

No.

when I did an offline javascript test, i realised that i need the <script type = 'text/javascript'> tag.

That isn't the case. Something else must have been wrong with your test case.

Douglas Crockford says:

type="text/javascript"

This attribute is optional. Since
Netscape 2, the default programming
language in all browsers has been
JavaScript. In XHTML, this attribute
is required and unnecessary. In HTML,
it is better to leave it out. The
browser knows what to do.

In HTML 4.01 and XHTML 1(.1), the type attribute for <script> elements is required.

<!-- HTML4 and (x)HTML -->
<script type="text/javascript"></script>


<!-- HTML5 -->
<script></script>

type
attribute identifies the scripting language of code embedded within a script element or referenced via the element’s src attribute. This is specified as a MIME type; examples of supported MIME types include text/javascript, text/ecmascript, application/javascript, and application/ecmascript. If this attribute is absent, the script is treated as JavaScript.

Ref: https://developer.mozilla.org/en/docs/Web/HTML/Element/script