What type of chili am I growing?

It looks like it may be a Chile de Arbol.

That could very well be the case. I've looked at pics and it is very much like those, but without the colour... Yet!

certainly have the typical chilli shape. The ones I grow are medium heat ones and look just like these green ones.

I was just researching the taxonomy of chilis. Far different from the last time I looked (twenty years ago?! Nah, I cant be that old! :D) when practically all were considered varieties of C. annua. DNA analysis has made a huge difference!

Thanks for the replies.

Seaburngirl: That is what I was starting to realize. I wanted super hot chillies :-(

Oh well, next year. Maybe I'm better off buying chillies and saving the seeds. At least that way I know I'm getting what's on the label...

well if you buy a ghost chilli and it is a named hybrid the seeds will not come true but it will be close to the species, but it may not be as hot as the ones you bought.

Not a modern hybrid, Sbg, but an old Indian landrace derived from a natural hybrid between C. chinense (Habanero & kin) and C. frutescens (Tabasco & kin).
Al, the problem with saving seeds from store-bought fruits is that you never know what kind of pepper they were growing next to on the farm. You might wind up with a cross with an Anaheim type! :)

so do they come true from seed as it is still a hybrid? your point was the one that I was making really; no certainty what you will get as an end result.

To make a long story short:
The actual hybridization occurred centuries ago. Since then, it has undergone many generations of selective breeding to enhance the characters that the Indian small farmers wanted, and is now genetically consistent enough to come true from seed. Almost every standard variety of produce on the market started out as a hybrid of some kind--often unintentional--and has since been bred into consistency.