Brian's answer is absolutely correct.

In everyday circumstances, the two terms could be used interchangeably and the meaning would still be intelligible.

If we look the underlying root nouns it can help to identify the subtle differences.

Supposition (n): "a belief held without proof or certain knowledge; an assumption or hypothesis."

Expectation (n): "a belief that someone will or should achieve something." 

So ...

"You're supposed to wait in line here" means that there is a general acceptance or assumption that waiting in line there is the correct thing to do. There's no specific expectation from any particular source.

"You're expected to wait in line here" means that some person (or group of persons), believes that you should wait in line there.

They are somewhat similar in the context that you used.   However there is a very small difference.  

Supposed to basically means need.  "You're supposed to stand here. "  =  You need to stand here. 

Expect is what other people think about what you must do.   "You're expected to stand here."   =   " The teacher/person/company/photographer thinks you should stand here."    

Also  we we use supposed to more than expected to.  I don't really use expected to that often.