There were a few innovations. Artillery of this period had abandoned the old gunpowder derivatives. This process had already been underway during the 19th century but was well advanced going into WW1. The move from gunpowder to smokeless variants based on nitrocelulose or Cordite actually burned slower than old gunpowder - which actually placed less stress on the barrel, allowing longer barrels with greater acceleration time and hence velocity and range.

It should also be noted that the steady improvement of artillery hasn't abated. Even today most battlefield casualties are caused by IDF(InDirect Fire) - though in modern, fast paced, low-intensity conflicts, small, more flexible mortar systems are the primary dealers of combat casualties today.

The long recoil barrel - where barrel segments recoiled and absorbed shock, allowing artillery to be fired accurately from fixed positions without having to be repositioned, or trajectories recalculated was another major technical innovation that occurred during the period.

However a lot of the difference came down to new doctrines of massed artillery. Even before WW1 artillery, when it could be brought to bear effectively, was very often decisive. During the 1870 Franco-Prussian War more, more effective and more effectively employed artillery being regarded as one of the major causes for a quick, decisive Prussian victory over the French Empire: a war most observers believed would be a long drawn out French victory. During this time concentrated German artillery demonstrated an ability, if they were unchecked, to completely annihilate formations and clear objectives by sustained weight of fire alone.

The result was that the steady improvements in effectiveness in artillery were being widely acknowledged by the end of the 19th century. Political and military leaders were both paying far more attention both to how much, and the relative capabilities of the artillery they could field vs their opponents - understanding that any disadvantage could be decisive - but also recognition that they required stockpiles of ammunition, manufacturing capacity to maintain massive rates of fire, and transport infrastructure to transport shells and guns to where they were needed.

I'm not sure this process would have been considered an arms race per se. But the buildup was conscious and steady and along a continuum of an artillery revolution that began in the 1600's when the first mobile artillery pieces began the process in which field army strategies and tactics began being shaped more and more by how well they countered enemy artillery and employed their own.

In either event, the result was that by WW1 there was a lot more artillery that fired shells faster, further than ever before. Training and doctrines evolved during this time around how best to employ these weapons.

Massed creeping barrages were a mainstay of WW1 warfare. Intense, concentrated artillery barrages, often involving sustained fire from hundreds or even thousands of artillery pieces, would be rolled forward, over enemy positions on set fire plans. These barrages were intense enough to effectively annihilate any infantry caught by them, and forced enemy forces to take shelter in hardened defenses. These barrages could often tear up the landscape, along with trench positions. The idea was for massed friendly infantry to advance, protected, behind the artillery curtain and assault the enemy positions as the artillery carried forward to the next line of defenses; ideally before the enemy could get back to their defensive positions.

The tactic was highly successful in some ways, however the damage done by them was one of the reasons WW1 dragged on as it did. As forces advanced, they outstripped their artillery - and it was challenging and sometimes impossible to move enough artillery and shells quickly enough over the destroyed landscape to maintain an offensive. This was the primary impetus for development of tracked, armoured vehicles that could traverse rough terrain & offered protection from high explosive and shrapnel shelling.

Much of WW1 came down to armies being forced to innovate, on the fly, the movement of men and materials on scales and under pressures for which there was literally no previous experience in human history to draw upon.

In terms of the type of artillery each side employed, this varied, but all sides had trouble finding enough artillery - and frequently made use of old, outdated guns as losses and need far outstripped capacity. I'm not an expert on the specific designs but my broad understanding is that while most major combatants modern artillery pieces were effective, the Germans are generally considered to have come into the war as the best prepared, and brought an effective mix of artillery: their reintroduction of high-arcing mortars, which could rain shells behind cover and into trenches were considered particularly effective.

Now a mainstay of modern fire and manoeuver doctrine, by WW1 mortars had been all but abandoned by major militaries in the world in favour of larger field pieces.

Tl;dr - there were many differences between artillery used by different countries, but number, supplies & getting the pieces they had moving was really the biggest challenge war planners seemed to face.