There are two primary types of garlic. Hard neck, and soft neck. The hard neck types usually have larger cloves, but fewer cloves in each bulb with a stronger flavor. The soft neck types can have a huge cluster of smaller cloves depending on the species, and it is the type they usually sell at stores since they store longer than hardnecks, but they generally have less spice than the hardnecks. I either buy them from bulbils which are kind of like seeds which take another year to reach full size, or I buy the cloves which cost more, but produce full sized bulbs when they are planted in the fall. The thing I love about garlic is that they really take no effort to grow as all I need to do is drop the cloves in the ground during the fall, and harvest them the following summer.
I grow both kinds and many species of them.
Starting with the hardnecks, here's Selvitta sunset started from bulbils
Here's the German red hardneck bulbils coming up. I'm finding that hard neck bulbils start out a little bit larger than softneck ones so they are much easier to grow from bulbils. The softneck variety that I've had all along produced tiny bulbils which take 3 seasons of growth to reach a full sized bulb.
Here are the Polish hardnecks which are getting pretty big growing from scapes. It seems like they need lots of water in order to maximize their rate of growth.
Here are the music hardnecks grown from cloves, and the foliage from hardnecks looks noticeably different than that of hardnecks. They grow taller, and grow much sturdier leaves.
Another hard neck species
Here's wild garlic which is supposed to be edible, but it looks closer to the onion family.
I have a few elephant garlics which grow huge, but they belong to the leek family and taste pretty bland. They don't really serve the purpose of real garlic as they lack the spice.
Here's another very large softneck variety, but this is a true garlic, and gets nearly as big as elephant garlic, but that's because they produce so many cloves which are not particularly big.
Finally here's my artichoke softneck garlic which I've had for many years, and they are the main type that they sell in stores, usually in sleeves of around 6 or 7 bulbs. The ones that I grow from huge cloves in my fertile garden beds often get much larger than their store bought counterparts.