Are potato starch and potato flour the same?

No.

Potato starch

Potato starch is made from the starch extracted from potatoes then dried to form a very fine white powder. When using potato startch it's easy to end up with a fine white cloud of starch in the air if you're not careful when transferring from bag to utensil. It is naturally wheat free and gluten free.

Potato starch is ideal for thickening recipes like soups, sauces, gravy etc. It has a neutral taste and is excellent for using in wheat/gluten free baking as it has good binding characteristics. It also turns clear after heating, making it ideal for transparent sauces.

Potato flour

Potato flour is made from whole, dehydrated potatoes. It is a heavy, cream coloured flour and naturally wheat free and gluten free.

Potato flour, like potato starch, is also ideal for thickening recipes like soups, sauces, gravy etc. It works well in wheat/gluten free cooking as it holds water in baked goods giving them a moister texture. It does impart the flavour of potatoes, but it's not generally overpowering or unpleasant.

If you use potato flour where potato starch is required in a recipe then your baking will turn out hard, unrisen, and nothing like the recipe intended. Therefore a wheat/gluten free kitchen should always keep both the flour and starch on hand. Keep them in the freezer, double wrapped, and they will maintain their freshness for a long time, potato flour does not have a very long shelf life otherwise.