System testing is nothing but end to end testing.There is 
no difference.

If i am wrong let me know.

end to end testing is like take login page enter loginid & 
password ,check the new mails my click on inbox after that 
signout means one transaction from starting to ending is 
called end to end testing. 

where as system testing is testing of the application from 
client view ,like funcational& non functional testing.

Systen Testing can be limited upto functional as well as non
functional testing of the System. Here in system testing we
test the application whether it is working according to the
SRS. Here we test for one module completely with all
techniques to test.
End-to-end testing all the interfaces sub-systems must come
into picture. All the end-to-end scenarios should be
considered and executed before deployment of the system into
actual environment. Here in end to end testing we test the
application whether it is working according to the BRS. In
End to End testing we test right from login screen and moves
to many other screens ( does its scenario) and logout of the
application, complete coverage.

End to End testing is to validate the flow of application 
fron the scratch to end and ensure all the functions are 
working properly.

system testing is validating the aplication as a whole 
using functional and non functional testing.