Collectible coins include various categories such as patterns and trial coins, which are experimental pieces created to test designs or minting processes. In the United States, specific examples like the 1861 fifty-cent patterns are highly sought after due to their historical significance and rarity. These coins often feature unique designs that were not adopted for general circulation, making them valuable to collectors and numismatists. The classification of these items can vary based on their condition, provenance, and the intricacies of their design.