What is the difference between plain flour and all purpose flour?

From the following site: Flour, Types of Flour used in baking, Buying and Storing Flour

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All-purpose flour is a blend of hard and soft wheat; it may be bleached or unbleached. It is usually translated as "plain flour." All-purpose flour is one of the most commonly used and readily accessible flour in the United States. Flour that is bleached naturally as it ages is labeled "unbleached," while chemically treated flour is labeled "bleached." Bleached flour has less protein than unbleached. Bleached is best for pie crusts, cookies, quick breads, pancakes and waffles. Use unbleached flour for yeast breads, Danish pastry, puff pastry, strudel, Yorkshire pudding, éclairs, cream puffs and popovers.

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You also might want to check out the site mentioned above and the one below for some excellent explanations about the various types of flours and their uses.

Kitchen Dictionary: flour

I RARELY bake and this answer helped a lot

I made lemon bars this year using all purpose flour. I made two recipes, because I was not satisfied with the first batch.
Previous years, I have used regular flour. They have always turned out perfectly.
This is what happened this year. The cookie "crust" crumbles and breaks apart when I cut into it. Both batches. The lemon custard filling is runny and doesn't set. Both batches.
For this reason, I would not recommend using all purpose and regular flour interchangeably.
I will go back to the regular flour next Easter.

All purpose flour is used for Indian Nan, cakes, Pizza, Bread etc. It is especially suited for biscuits, muffins, cakes.
Simple flour is whole wheat flour.

Whole wheat flour and "simple flour" are two entirely different things.

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Originally Posted by daschreck

I made lemon bars this year using all purpose flour. I made two recipes, because I was not satisfied with the first batch.
Previous years, I have used regular flour. They have always turned out perfectly.
This is what happened this year. The cookie "crust" crumbles and breaks apart when I cut into it. Both batches. The lemon custard filling is runny and doesn't set. Both batches.
For this reason, I would not recommend using all purpose and regular flour interchangeably.
I will go back to the regular flour next Easter.

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If by "regular" flour you mean "Self-rising", then no, you shouldn't use all-purpose flour in place of self-rising flour if the recipe calls for self-rising. Self-rising flour has leavening agents and salt in it, whereas all-purpose does not. If you look at the package labeling, it will tell you what's in it, and all-purpose flour contains nothing but flour.