Hum, I haven't ever heard a tart labeled "regular". So I'm having a hard time following your question. But the differences in tarts usually is in the dough or if it has been baked in a tart pan or with-out one.
If you could restate your question with more detail I'll do my best to help you.
I might be stepping out on a limb here but most of the recipes that I have seen labeled as classic usually consist of a crust, as mentioned above a sweet dough such as pate brisse, pastry cream & fruit covered by a glaze such as melted apricot jam. Most of the recipes also include a layer of frangipane (almond cream) baked with the tart shell.
It's really funny as I would guess that this is fairly modern compare to the rustic tarts or the savory tarts which have been, as said above, around a long time.
The term "Classic" refers to a type of tart that everyone recognizes as an old time/world treat. A style or recipe that has endured for generations, usually more simple and simple ingrediants made in a very traditional style, baked in a traditional style of pan.
A "Classic Lemon Tart" would have a traditional filling of lemon curd, a pastry crust, baked in a fluted tart pan. A "Orange-Mango Tart with a Rustic (free formed) Lemon Thyme Scented Crust." Orange and mango is not a common combination, herbs in a crust is not usual, and this recipe does not use a tart pan, the crust is formed on a baking sheet and folded over the fruit.