As far as I've read or experienced, I don't know the difference between naan and pita bread.  Regarding ingredients, they are both enriched, leavened (w yeast) flat breads.  The enrichment is often milk, butter and/or yogurt (@CocktailStat even uses sour cream!) and sweetener honey or sugar.  Regarding method, pita is often baked while naan is supposed to be made in a tandoor oven.   The other significant difference is in form, pita is thicker and naan often much thinner so as to use as a flexible scoop for food.

I've posted on this type of flatbread a million times - I love them because they're tasty and fast to make, no need to warm up the refrigerated dough.  I've done them on the stove top, and again on the stove top, and baked them in a ridiculous oven I made.  Some I've started on the stove top and then tossed them in the broiler to finish.  These methods aren't bad, but I wanted something better, better color and texture, faster bake on the outside to leave the middle super soft and tender.

Having studied a few diy tandoor ovens on YouTube, I identified the tandoor's critical components: a super hot surface with high contact to the dough and an exposed heat source that sears the other side of the dough.  The broiler!  I placed a 15" diameter cast iron pan on the middle rack, and heated the oven to 550F on broiler setting - this means only the top element is on.  Your oven must be damn clean to do this.  With the cast iron in place - I did many, many trials.

1. Dough made of milk 180 g (3/4 C), yogurt 20 g (1 T), butter 12 g (1 T), sugar 10 g (2 t), salt 5 g (1 t), Fleischmann's instant active 3 g (1 t), unbleached white flour (Montana Sapphire or Gold Medal unbleached white) 300 g (2 C + 2 T).  Mixed/kneaded in a bread machine and left in fridge overnight.

I rolled a 50 gram piece to a 6" diameter, let it rest a few minutes and tossed it on the cast iron.

Bubbled within a few seconds.
 The dark side was on the surface, the other side only a few flecks of brown.
 Thin delicate layers.

2. You can roll it too thin.  I rolled a 50 g piece to a 10" diameter and made a cracker.

I also placed the pan as close as possible to the broiler element; it wasn't all that different than baked mid oven.  So the top element preheats the pan enabling a nice browning of the bottom, then the top gets browned, albeit with a little lag.  Not sure how to remedy that.  Still some work to do.

So, this method is a single toss on the hot surface, remove and done, about a minute per bread.  And for the small ones, I can make a bunch at a time with the big cast iron surface.

I did chapathi on here too, but ate it too fast for a pic.  Chapathi dough is atta flour 100 g, water 60 g, salt 1.5 g - that's it.  They are wonderful cooked like this.  Better than stove top.  Pics later.

I think this method is also amenable to cracker thin pizza and crackers, there are a lot of variations in ingredients and forms to try.  If you don't have the cast iron disc, try a dark enamel on steel sheet.  Enjoy.