Espresso grind or filter grind: this is the difference
Espresso is made under high pressure in a short amount of time. This means the water should be met with some resistance, so it will absorb the aromas well. The grind is tricky, because if it's too coarse, the water will run through it too fast, resulting in a weak cup of coffee. If the grind is too fine, like dust, the coffee will run through too slow and end up tasting bitter. That's why you should use a fine coffee grind for espresso.
Quick filter grind
Quick filter grind is less fine than espresso grind and can be compared to coarse sand. When making coffee on a filter machine, there's no pressure involved in the extraction, meaning the water has to be able to drip through the coffee easily. This means the taste of filter coffee is always less intense than that of espresso, and no crema will appear, since it only appears under high pressure.
The best one for you?
This means the eventual result in your cup depends on the extraction, which stands or falls with the right coffee grind. Remember that water will have an easier time of dripping through a layer of boulders than through a layer of sand, because there's more space in between them. It works the same way with coffee: the finer the grind, the longer it takes for the water to run through. In an espresso machine, the water is pumped through the coffee, meaning the resistance should be a little higher in order to prevent weak coffee. In a filter machine, the water should drip trough the coffee, meaning you should help it out with a coarser coffee grind, i.e. quick filter grind. It's a good idea to get your beans ground at a specialty store or start experimenting yourself using a coffee grinder.