Well, if you were a QA Engineer by the standards used for software engineering you would design and implement tools that facilitate QA, whereas a QA Analyst would be a key user of those tools in the process of analyzing test requirements, test case design, test scripting, and test execution.
If you were a train engineer you would analyze a number of factors to bring the train to a proper stop to allow passengers to board. The analysis process might be different, but the stopping is not a random occurrence, and braking must be done in a gradual manner so as to not turn passengers into projectiles. So there you have it, Rich is quite right to point out how different cultures attach a different meaning to the same terms.
In my part of the US, an QA Analyst works with computer software, and a QA Engineer has an engineering degree, and may test both hardware and software. The 'QA Engineer' job description will specify the type of engineering degree required.
Terms vary from region to region, however, and I have seen many cases where the terms are interchangeable.