Hi

In both Tests we perform Load and Performance Testing.

Testing the application in intranet(withoutbrowser) is an 
example for client -server.(The company firewalls for the 
server are not open to outside world. Outside people cannot 
access the application.)So there will be limited number of 
people using that application.

Testing an application in internet(using browser) is called 
webtesting. The application which is accessable by numerous 
numbers around the world(World wide web.)

So testing web application, apart from the above said two 
testings there are many other testings to be done depending 
on the type of web application we are testing.
If it is a secured application (like banking site- we go 
for security testing etc.)
If it is a ecommerce testing application we go for 
Usability etc.. testings.