Are flat bows much different than long bows?Faster,slower,more forgiving,shorter,longer,same length,etc...?

Good question--I see the terms used interchangeably.  I think a selfbow is technically any bow made by "self".  A longbow is, technically, a non-recurved bow that is a certain length or longer.  A flatbow is a relative term used to describe a non-recurved type bow that has a relatively flat cut-away profile.  Or maybe a flatbow can be recurved?  Not sure.

Then there is the issue of whether the bows in question are laminated or solid wood, because a solid wood bow might have to be proportioned such that it is inherently slower than the equal laminated bow that has smaller proportions and therefore faster speed.

You could have a flat longbow or a non-flat longbow and it could be solid or laminated, etc. etc.

I have a feeling others will have slightly differing views on all this.....

I think flat bows are just longbows that are a bit wider in limb and a bit shorter. Longbows tend to have a narrower limb.

It really just means what it says, flat, as in cross-section.  This is in contrast to a "D" or more round shaped cross-section.  

A flatbow can be a longbow.  Europeans often consider a flatbow to be the same as an American Longbow.

A longbow is differentiated from a recurve bow in most cases.  It has little to do with actual length.

As for the pros and cons, as always, that depends on who you are, how you shoot, what you expect from archery and yourself.  On average, a bow is a bow is a bow.

Well Said John!!  

Not an expert but I will give it a shot.  Self bows have no glass, and I think no backing.  I could be wrong on the backing, but mostly they are just wood.  Long bows are long and have narrow and deep limbs.  Flat bows have thinner wider limbs like curves, but with a longbow shape.  Hybrids are whatever you want to call them, and it depends on if you are a purist longbow type.  They are called hybrid, longbow, semi-recurve, R/D (or is it D/R)  long bow........... , but typically the hybrids are more a R/D flat bow or semi-recurve.  Where to draw the line between the R/D long bow and hybrid is hard to always say from what I read.  Some take into account the grip and some only the limb.  If it is a three piece bow it is a hybrid, or maybe R/D flat bow due to the limb shape required to bolt it on a riser.

I call anything a longbow that is not a recurve.  That keeps it simple.  My Firefly is a hybrid, but you could call it a R/D flat bow.  My MOAB I see as a R/D longbow.  The Lost Creek is a hybrid and I could be talked into a semi-recuver on that one.

The original question was not actually about selfbows, but flatbows.

They have been described acurately already.

As for drawing and shooting characteristics, John said it best. I would add that a flatbow sometimes draws real smooth, but the recovery at the end of the shot is not as nice as a longbow with a deeper crossection. The deer won't mind either way.

OK, I consulted the world authority on the subject and it looks like:
Selfbows are considered any bow made from solid wood, no backing.
Longbows are generally considered a bow as tall as a man, or longer, with D or round profile.
Flatbows can be solid wood or laminated but have the relatively flat profile when compared to a true longbow.

So the answer to the original question is, no, not much different, just different in profile.
As far as performance, feel, forgiving?  No.

flatbows are the ones you lean against your truck and then back over them. Wish I had a picture to show you.

Well, ya'll have nailed it, the only thing I would add is that a recurve has string groves on the limb.  I know that was not in the question, but it was brought up later.  

That is what differentiates the bows in a tournament.  Well in my neck of the woods anyway.  There was a big stink about this when all the hybrids started showing up.  Some of the longbow shooters did not want them in a longbow class and some of the recurve shooters did not want them in a recurve class.  What it amounted to is that some of the better shooters had a hybrid bow and the other guys did not want to get beat.  They were better shooters, it had nothing to do with the bow they shot.  Some people just can't take a lickin'.

Thank-you,Kinda what I thought.It feels good to be sure about it.Could not have done it without all of you.

I always thought that on a recurve, the string touches the limb, on a longbow, it does not.

A selfbow is one where all the work is done by the same material from back to belly.  It doesn't strictly have to be wood.  It could have an aesthetic or even a splinter preventing material on the back.  If the backing takes over any of the tension work, it isn't a selfbow.  Sinew is definitely a backed bow.  Bamboo makes it a composite.  A wood veneer could simply be aesthetic.  Rawhide is debatable.

this is easy, and mentioned above several times.

flatbows have flat limb cross sections.  99.9% of all american built longbows (reflex, mild r/d, aggressive r/d) are all flatbows.

'real' longbows have limbs with 'D' cross sections, meaning the classic english longbow (elb).

modoc indian style flatbows are self or board bows with very wide bases and narrow tips.  these limbs have very flat cross sections and the length view looks quite tapered and triangular.

is there a difference in durability or longevity?

all things being equal, no.