Short Summary of Differences in Grind Level
Grind for Espresso (Extra fine)Espresso requires a fine grind, because water needs to pass through the coffee quickly for full brew extraction. If the grind is too coarse, the coffee will be under extracted and have sour flavors, if it is too fine it can be over extracted resulting in bitter tasting coffee. Moreover, the machine used to brew espresso must use high pressure to push water through the ground coffee. A fine grind will clog excessive amounts of water at once and lead to over extraction. A proper espresso grind size should look like powder or sand
Grind for Paper Filter (medium-fine)As long as your coffee is ground fine enough to filter through a paper filter without clogging it, this grind level will work fine. The powder/sand consistency of an espresso grind is not necessary with a paper filter. Furthermore, some paper filter makers recommend a slightly coarser grind to achieve better saturation. A medium or coarse grind would be good for a paper filter.
Grind for Nel Drip (Medium)The grind level should be similar to that of a paper filter, but it's okay if the coffee is ground slightly finer because nel drip brewers have a fine cloth filter. If your coffee grounds are too coarse, they will leak out of the brewer and you will get coffee grinds in your cup.
Grind for Siphon (medium-coarse)For this brew method, the coffee is brewed using two separate chambers that are then combined to form one beverage. The siphon requires a slightly finer grind size than most other methods because you can't control when the coffee completely dries out in the wells of the filter chamber. If the grind is too coarse it will clog up the filtration system and cause overflow or slow drainage through your grounds. You don't want these things to happen because they are messy and bad tasting, so be sure to use a fine enough grind size
Grind for French Press (coarse)
This type of brewer uses gravity to push water through ground coffee by plunging down on top of it. This means that the coffee must be ground coarse enough to allow water to pass through it quickly, but fine enough so that no sludge or grounds go into your cup. A medium-coarse grind works well in this brewer for this type of drip control. In addition, a coarse grind is ideal for brewing French press because it creates a stable bed for the coffee to step in.