What is the difference between a change in quantity supplied and a shift in the supply curve?

There are a few different ways to think about
this.

Graphically, a change in quantity supplied is simply
a movement along a given supply curve.  The curve does not move--it is just that you
move from one point to another on that curve.  By contrast, a shift in the supply curve
involves the whole curve moving.

Another way to think about
it is to say that a change in QS is caused by a change in the sale price of the product
we are talking about.  If the price that you can get when you sell fish changes, the QS
of fish changes.

A change in the supply curve, by contrast,
means that there will be a different amount of the product offered for sale
even though the sale price does not change.  When the
supply curve moves, it means that something else has happened.  Perhaps, for example,
the price of the fuel for fishing boats has dropped.  If that happens, fishermen will
supply more fish even if the sale price of fish does not
change.

So a change in QS is a movement along a curve that
is caused by a change in the sale price of the produce.  A change in supply is a shift
of the curve that is caused by something other than the sale price of the
product.