Duties of a QA Engg.
Generally a QA Engineer and a QA Tester would mean the same 
in real time environments.
However, when it comes to hierarch levels..
QA Manager will have QA Test Lead under him and QA Test 
Engineers under the lead..
General Duties of the QA would be:

1. To collect all the docs like: BRD(business req doc), 
technical tp, functional tp from the management or QA 
manager.
2. To review the above docs.
3. To moderate the FTR (Formal Technical Reviews)
4. To write RTM
5. Design Test Cases.
6. Once the build release to QA, begin the testing
7. Log the defects in teh Defect tracking tool.
8. Conduct client meetings.., review defects with the dev 
team and demo the defects to the developers if required.

The above are in general and can be disscussed in detail 
further.

QA: Verification
QC: Validation.

QA means to avoid the Defect.
QC means to prevent the Defect.

QA is related to Process.
QC is related to Product.

Following are the duties of QA/QC Engineer:
identifying Test Scenarios based on SRS
Involving in black box testing.
Performed Functional and Regression Testing.
Execution of Test Cases and generating Reports.
Defect Tracking and classifying them based on severity.
Bug reporting.