With a slash, you drag the edge of the blade across the target, making a wound that is quite shallow compared to the depth of penetration from a piercing attack.
...The attack you described is a draw-cut. Not a 'slash.' Slash and Cut are generic terms for the way you swing the weapon, with an arc, rather than pushing it forward, as in a thrust. A chopping attack is a cut - it is a slash. Eh.