The sulfur compounds are released as soon as we cut into a bulb of garlic and expose the inside surfaces to oxygen in the air. More chopping will release more of the compounds, so it follows that minced garlic and garlic paste will have the strongest taste.
We use garlic paste and minced garlic in dishes where we want a strong garlic flavor permeating the dish. The small little pieces will also dissolve into the other ingredients over long cooking, leaving sauces smooth and evenly seasoned.
Whole garlic is at the other end of the spectrum. Since the sulfur compounds are never forcefully released, whole garlic will simply add a subtle and slightly sweet garlic flavor to dishes. Crushing the cloves releases a little of the sulfur, making the garlic flavor a little stronger. Roughly chopped garlic dials up the flavor yet again.
Changing how finely you chop your garlic is one way to control the garlic flavor in your dish. You don't necessarily have to follow the recipe! Next time you make a stir-fry or pasta sauce, experiment with different levels of garlic intensity and see if you can tell the difference!
Do you love strong garlic flavor in your dishes, or do you like it more toned down?