the differences between a right handed double and a left handed double?

thanks in advance Jarrod.

One is for people who are right handed and the other is for lefties.....Sorry couldn't resist.

Soemone else could probably explain better but it is pretty simple, they are mirror images of eachother.

Jarrod,
Aside from the obvious, left hand cheek piece and triggers turned for the left hand. I was told a true lefty fires the left barrel with the front trigger and the right barrel with the rear trigger.
I don't know the advantage. My double has a lefty cheek piece and lefty turned triggers and fires the right barrel with the front trigger and the left barrel with the rear trigger. Other than show I don't know the purpose.

A true left handed double is a mirroe image gun. The front trigger fires the left barrel, the stock has cast on rather than cast off and if it has a cheek piece it will be on the right side. The top lever will also work in the opposite direction and the lefty shooter will draw it just as a righty shooter would for a right handed gun.

I have been told that a benefit to the true left handed gun for a lefty shooter is that when the front trigger fires the left rather than the right barrel the recoil torque will move the heavy kickers away from a lefty's face, where as a right barrel first shot will move the rifle into the face.

I am a lefty and I prefer a right hand action stocked for a lefty and with the triggers merely twisted to accomodatew a lefty. But this is because I grew up with modified righty guns. I was in my thirties before I ever saw a true left hand gun and by then I found it awkward since I was so accustomed to adapted righty guns.

JPK

Isn't there some thing to do with "cast on" or "cast off" also, to give the natural point as in a good bird gun?

Ok on a lefty is the front trigger on the right or left?
And what is cast on and cast off?

Cast Off - An offset of a gun stock to the right, so that the line of sight aligns comfortably with the right eye while the butt of the stock rests comfortably on the right shoulder. Almost all right-handed shooters benefit from a little castoff and most custom built guns are made this way. The only question is how much. The castoff of a gun is about right when, with the gun comfortably mounted, the front bead lines up with the center of the standing breech. A stock offset to the left, for shooting from the left shoulder is said to be Cast On.

The above is a quote from the
Terms and Abbreviations of Hallowell and Co. It is a good source for the terms you are looking for.

A completely left handed, mirror image rifle will have the top lever opening in the opposite direction, the front trigger firing the left barrel and cast on to the original owner's specs, or changed afterwards and the cheekpiece, if there is one on the right side of the stock.

But most lefty rifles (and shotguns) I have seen are right handed rifles stocked for a lefty and the triggers just twisted for a lefty. I think this is because the lefty fellow grew accustomed to right actioned guns growing up and then had one built for him, or altered for him on a righty action. This is how it worked for me. I grew up shooting righty hand me down guns til after college, when I started figuring out how to make a gun fit. Also there are tons of right action guns around and very few left action guns. Some sidelock rifles and shotguns have the cast beginning in the locks, these often have lots of cast off and are ussually unsuitable for a conversion to lefty, but most others will convert fine - right action but stocked for lefty, triggers twisted for a lefty.

FWIW, I have become so accustomed to a righty action that I find a pure left handed gun a bit awkward.

JPK