Garlic: minced, crushed, chopped, sliced. When to use each one, and what is the difference?
Dice or slice when the garlic will be consumed along with the other ingredients.

Crush in order to release more flavor. If you add it whole it can be removed afterwards.

Make paste when you don't want it to be visible and all its flavor to be strong and evenly distributed in the dish (e.g. hummus as it is a paste itself, you wouldn't want it to have little lumps in it).

Use whole garlic cloves in slow cooker, and it will release its scent and flavor with time. You can remove it afterwards, the flavor will be there regardless.

Processing it before adding other ingredients, makes it release its scent and get mild-flavored.

All methods except processing will add strong flavor to your dish. The paste will be the strongest, as you consume all of the garlic.