Difference between wreath, garland, and laurel

The choice between wreath and garland is simple: a wreath is round, while a garland is a long string.

A laurel wreath is a specific type of wreath, made of bay leaves. It is generally intended to be worn on the head. Most other wreaths are meant to be decorations, e.g. on a memorial/tombstone or on a front door (Christmas wreath), although there's also the practice of young girls/brides wearing wreaths of flowers.

If I'm talking about an actual physical object, I'd generally say laurel wreath, not laurel by itself. If I'm using the term figuratively, i.e. to mean accolades or rewards, then laurel or laurels by itself will usually get the point across.

All three of those are made of the same thing, but they have different uses and typically different sizes.

This here is a wreath. Notice that it's a ring, and it's way too big for most people's heads. Notice also that it's rigid, and used as a wall decoration.

This is a garland. Note that it's a long, flexible strand rather than a rigid ring.

And this is a laurel. Note that it's small and mostly flexible, and is suitable for being worn as a crown or circlet, unlike the other two.