I believe its Genovese. I had some basil that grew only to about a foot tall, and was bushy as opposed to tall stalks. The leaves were quite small too, compared to regular basil. The type you have would probably grow into that same size. It also is fairly slow to bolt to flower stalks on the tips of the branches. Once the basil is planted outdoors in the sun, the leaves will get a little bigger.

After reading your description I believe ksrogers, sounds like Genovese, I think there is also a dwarf variety of that, maybe its all dwarf. Either way it's the smallest Basil I have seen.

Genovese is a regular leaf type similar to Large Leaf Italian. What you were given seed for is more likely Spicey Globe or another new dwarf variety of many new types arriving every year. Taste a few leaves and see if it is pleasing to you. Some small leaf types have a distinctive off-flavor.

We found that most people prefer Genovese to all of the variations. We had to compost a few hundred pots of the Spicy Globe basil plants last year. They looked very attractive in pots but most customers didn't care for the flavor.

They do seem like some sort of dwarf variety, since they are so short, but very very bushy. The leaves taste good - like regular basil. I've made a few tomato/mozzerella/basil salads with them and the small leaves work great; I just tear them off the stems and through them in, they are the perfect size.