Difference between testing done by the testing team & by 
developers can be cosidered the almost same as Black box & 
White Box testing.
 Main feature of individual test team testing is that the 
testing team is that the test case selection is based on 
the analysis of the specification of a component without 
any knowledge of the internal working.System testing is a 
example of this.  
And as that of the white box testing is where the test case 
selection is based on the internal structure of the 
component.Integration Testing is an example. 
Unit testing being a pefect Example. 
Unit testing is a procedure used to validate that 
individual units of source code are working properly.

The above explanation is right but i would like to add some 
thing in it.
The testing done by developer is unit testing and the part 
of white box testing. The aim of the developer's testing is 
to check that his code module is working. He always test 
keeping the positive aspects of his code.

but the tester test keeping himself in the shoe of the 
user. Testing positive side of the functiolity he also test 
for the negative functionlity in order to check that the 
program should not bahave like that when worng input is 
provided which it should not be.