There are two kinds of Thai basil. The usual one--and the one I assume you have--goes by the Thai name horapa. It is a variety of the same species as European basil, but the leaves look different and it has a different aroma profile. The fresh leaves (bai horapa) are used in Thai cooking, particularly in larb (spicy salad) and in stir-fries. One can substitute European basil for horapa at a pinch. I imagine it could work in the opposite direction, too, but I've never made pesto using bai horapa.
The other kind of Thai basil is holy basil, called krapow in Thai and tulsi in Hindi. It's a different species of plant (
Ocimum sanctum) from European basil and horapa (
Ocimum basilicum), but the two are closely related. It has a more minty character than European basil. The fresh leaves (bai krapow) are used in stir-fries and some noodle dishes. Holy basil starts wilting as soon as it's picked and so the fresh leaves are hard to find in the marketplace because of their short shelf life. Most restaurants and home cooks substitute horapa for krapow.
I posted a recipe for Thai stir-fried chicken with chiles and holy basil
here. You can substitute bai horapa for the bai krapow.
-Paul W.