Polynomially related encodings
Yes, it's correct that you can convert between base-2 and base-3 representation (in either direction) in polynomial time.  Thus, that would be a good example of two encodings that are polynomially related.

You can't convert from binary (base-2) to unary representation in polynomial time; it causes an exponential increase in the size of the instance.  That's probably what is meant by "expensive".