When a recipe calls for a cup of flour, does it make difference, if you use either all purpose; or self rising flour ?

Depends on what your making.
I use self rising in many dishes.
I don't like that back taste on baking powder

What makes self rising flour self rising? baking powder and salt are already added (probably more than you would add for any recipe)
" Making self-rising flour at home is easy. Just use this basic formula: For every 1 cup of all-purpose flour, add 1 1/2 teaspoons baking powder and 1/4 teaspoon fine salt. …"

If your recipe calls for baking powder, things like biscuits or pan cakes, then you can use the self rising flour and leave the baking powder and salt out. If you are making something that does not need backing powder, like pie crust or gravy, don't use the self rising flour.
But you can use all purpose flour for any recipe.
Although I'd rather have a hard wheat flour for any yeast or sour dough recipe.

Well, we won't go off the rails and bring in the myriad of other flours besides all purpose and self rising. Self rising is the "easy button " for most recipes and the one most commonly found in kitchens across the country. Having been a pastry chef in a former life I can tell you there's far more options than those two, but more specialized in their intent.