What is the difference between tank and self propelled artillery?

Answer 1

A tank can fire on the move a spg must stop and fire.

There are more ways to define this but this is the simplest way to understand it

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I'ts a good way to answer, but the SPG don't need really to stop to fire, but stand and fire is mostly common because the gun recoil can easily injure or kill who is firing the SPG...

So, what is the difference between one SPG and one Tank?

First: Tanks need to be very agile or very armored, and the SPG's just just need to move, many times regardless of the speed or the armor, so the most of the SPG's don't have a tower and the armor is less than 60mm...

Second: Tanks are mobile Cannons, and SPG's, mobile Howitzers. A Cannon is a device capable of firing projectiles at enormous speeds, that sometimes don't need a explosive charge ( at least against other tanks ). A Howitzer is a device, that unlike the Cannons, is centered in the explosive charge, having a minimal propeller charge, that will most of the times help instead of stuck, because SPG's most of the times will fire in an arc trajectory, and in the direction of the infantry, not of other mobile steel pieces.

So, for don't have confusion, Howitzers are degree-ed artillery with enormous firepower and Cannons are horizontal and high speed ones. Tanks and SPG's are just mobile counterparts of both, with some other differences.

Source: World of Tanks Wiki.