In normal transistor operation, the emitter is where the electrons spill over from into the base, and they cruise across to the collector (so in fact the positive current goes from collector to emitter across the transistor).
In our simplified npn sandwich picture of a transistor, the situation looks symmetric, and looks as if the difference between collector and emitter depends only on the applied bias: base to emitter corresponds to the forward-biased side and base to collector (or emitter to collector) corresponds to the reverse-biased side. However for real-life transistors, it does matter which terminal is which-- they are designed for the current to flow in a particular direction. (The arrangement of semiconductors inside a transistor doesn't necessarily look like the conceptual sandwich diagram-- design of these things is a whole subfield of engineering well beyond the scope of this course!)