First, the difference between minced and chopped garlic can have a big impact on your cooked dish. A "mince" is finer than a "chop", and here's why it matters. If you use chopped garlic, which is bigger, in a dish that calls for minced and doesn't cook very long, you will likely be eating raw and pungent garlic.
A garlic press makes a paste of the garlic with more of the garlic oils released. Very finely chopped, or minced garlic is less than 1/16 inch in diameter, like course cornmeal. Chopped garlic is typically no more than an 1/8 inch.
The good news is that many grocery stores now sell bottled minced and chopped garlic. While nothing beats fresh, when the garlic is a seasoning and not a major source of the flavor of the dish, the bottled makes a decent short-cut. Just be sure to read labels and look for the brand with little or no added ingredients.
See 7 Ways with Garlicfor a variety of uses for garlic.