Originally posted by Heyesey
All of the terms you posted actually describe what the weapon is used FOR, not what it actually IS. So it's not really feasible to say "Tanks are xyz; tank destroyers are abc; assault guns are pqr." Depends who built them and what they had in mind at the time.
"Artillery" is a sweeping term meaning any weapon that fire projectiles at a distance. Strictly speaking, you could class a pistol as artillery; certainly all of the other four classes you posted count.
The original "tank" concept was simply an armoured car that ran on caterpillar tracks, to handle all terrain, and was sufficiently armoured to withstand machine-gun fire so that it could get across no-man's-land without everybody in it being killed. Basically anything which is fully-armoured and runs on caterpillar tracks is a tank. Some tanks are tank destroyers; all tanks are self-propelled guns, unless you build a tank with no weaponry. A tank which is used to assault things is an assault gun *and* a self-propelled gun, and also artillery. If it's used to assault other tanks, it takes the nap hand.
Hope that helps 
Weeeeeellll
What any kind of equipment looks like, and what it's supposed to be used for are usually closely related (except some British tanks of early WWII, I suppose ;-)), and you can't discuss one without mentionning the other. That a specific design can be used in other roles than the one originally envisionned doesn't change what it basically is.
Take the German 88 Flak 36 gun: that it could be (very) effectively used in an AT role, and even in some cases as light artillery, doesn't change the fact that it was primarily an AA weapon. When the Germans realized how good it was against tanks, they redesigned it as an AT gun and thus was the Pak 43 born.
Artillery: although any definition has its gray zones that can be stretched, from the late XIXth century onward, artillery is basically understood as thingamacallits intended to fire big shells for area effect. Sure you can argue that strictly speaking the big fortress can openers are closer to AT guns than this definition of artillery, but just as any red-piping wearing guy would lough out loud at classifying a 400mm siege mortar alongside a 37mm AT gun, so will I. War is about practical matters like life and death, not entomology.
Going back to origins, tanks evolved from two radically different concepts.
In Britain, stretching matters a little, it can be said that presented with the problem of a large land conflict, the British tried to adapt what they knew about - naval warfare - to land operations, thus the concept of the Land Battleship. It's not by chance that the first designs came from the Navy - Churchill liked gadgets, too, and it helped.
In France, the idea emerged after the spring 1915 battles. It had been observed that attacking infantry fared reasonnably well as long as their attack could be coordinated with artillery.
With early XXth century technology, this point was quickly reached: without radios, once infantry left their trenches, they also left telephones and contact with the artillery behind them, so as soon as the preplanned fire plan became irrelevant due to the ennemy doing unplanned things - which usually happened within minutes of H hour - the infantry were left to their own devices and suffered badly.
Also, even assuming the first assaults went well, since the second lines were usually out of sight of the starting trenches, once the first line was breached, there was no way to support the second stage attacks with efficient arty fires.
A possible solution to this was to find a way to let guns accompany the assaulting infantry so they would enjoy continuing arty support all along the way.
Thus were the Schneider and St Chamont born: take the good old 75, put it on tracks so it can cross No Man's Land, and while you're at it, why not encase it in armor?
Properly speaking, those first French tanks were assault guns, and the first French tank units were called Assault Artillery. What are today called Battle Tank Regiments in the French Army trace their history to those Assault Artillery Regiments of WWI, which were numbered in sequence with regular artillery regiments.
Although those two early models had many design faults, the basic concept was sound, and evolved into the german Sturmgeschütz, the Soviet heavy SU series; with the start of WWII and new credits, the French army had by June, 1940 a prototype that closely resembled the Stg.
As the first disappointing uses of tanks happened, General Estienne, the man behind them, had a talk with Louis Renault, then probably the largest carmaker in the world.
From what a carmaker had to say about the fledgling tank's design emerged the FT-17 light tank, the first and only of the WWI contraptions that can be recognised as a tank from today's point of view.
After the first battlefield experiments with tanks, the two acknowledged - I'm not implying they weren't heavily debated - uses of tanks were infantry support and independant operations behind ennemy lines. I'm not aware that anybody before WWII thought that the best AT weapon could be a tank.
So, based on WWI battlefield experience with IS tanks and a lot of untested theorizing between the wars, everybody went to war in 1939 with a jumble of mostly inadequate designs.
With the advent of battlefield realities, what could be done with putting guns on tracks became a bit clearer. Some existing designs could be adapted to fit those uses, others had to be created, but remember that there was a war going on, so the priority was more to give the troops something useful quickly than getting designs which perfectly fit the new doctrines - and those doctrines were perpetually evolving anyway.
Given those constraints, it is possible to argue endlessly about how a specific model should be classified.
In which category does the Sherman 105 fall, for instance? It was made to fill the assault gun role, but except for its gun it is an M4 medium tank.
M7 Priest SP howitzers, designed as self-propelled artillery, were often used with open sights as assault guns.
There are examples of M4 units pressed into indirect fire artillery missions.
The Mathilda II was often used as an MBT although it was intended as an IS tank.
And I could go on like this for a long time...
In fact, the results of WWII battlefield experience are today's AFV's.
The tremendous increases in armor soon required guns so specialized in defeating armor that they became more and more useless against unarmored targets.
Furthermore, the ever-increasing number of AFV's on the battlefield, the ever increasing size of the projectiles needed to defeat them and the limited space inside an AFV meant that the typical ammo complement could only include a very small number of anti-personnel shells.
So the modern MBT's gun is mostly an AT weapon, and tanks have to rely on MGs against infantry.
On the other hand the WWII-vintage halftrack evolved into the modern IFV which combines the features of the APC and the original IS tank.
Towed AT guns have disappeared from Western inventories as too easily dislocated (in the maneuver warfare theory sense). Their role was taken up by AT missiles.
Improving technology lets SP artillery provide the infantry with close supporting fires almost anywhere and at any time. Combined with the advent of the IFV for very close range support, this has eliminated the need for assault guns.
There's little doubt in my mind that should a major, protracted war happen again, we'd see the German-style TD back, simply because it's simpler and cheaper to build than turreted tanks and almost as efficient in lots of situations (the one of Suvorov's assertions that I can believe is when he says that the ever-practical Soviets went on secretly building TD versions of many of their MBTs).
Some form of assault gun might also reappear when somebody starts to realize that the almost supernatural efficiency of modern artillery is entirely dependant upon both the presence of fragile GPS satellites and easily disrupted data-intensive radio communications.
Wow! what a post! did you really read it all or did you jump straight down here?
