Garlic is grown from either cloves or bulbils - normally cloves. Bulbils [the small bulbs formed in the "flower" (it's not really a flower) of a hardneck (or "scape-forming") garlic scape] are vegetative clones, the same as cloves, but they are smaller, there are more of them, an they have no soil contact if properly handled - as such, bulbils may be used when looking to quickly increase stocks (many more offspring from a single plant) or to break disease cycles (no soil contact.) Otherwise they are often cut off well before full bulbil formation, both as a secondary crop, and to encourage larger bulb formation. Depending on the size of the bulbils they may take 2-3 years to form a full-sized plant (smaller ones tend to produce a "single-clove" the first year (or two for ones that are very small), but if that is replanted normal full-sized garlic will result.
In my experience spring-planted garlic has always been inferior in yield to fall-planted garlic, so if you are planting now, I hope you are in the Southern hemisphere.
Typical practice is to plant seed cloves in the late fall and harvest in summer. For maintaining stock I tend to save the best 20-25% or so of heads for seed stock; (I maintain about 100 heads at present, which means I get 75 or so and plant the larger cloves from 25 or so) when trying to increase stocks you will need to save more heads for seed to get more heads the next year. The larger the clove, the larger the resulting head of garlic, all else being equal.