Asking me what types of orchids there are is like asking me what types of people there are. Well, there are tall and short people, smart people and not-so-smart people, introverts and extroverts, people with different skin colors, and people from different parts of the world. Likewise, you will find many different types of orchids—different colors, species and hybrids, miniature and standard-sized, all different genera from different parts of the world. So I will narrow the question a bit, and look at it in terms of the orchids you will likely to buy and grow.
The vast majority of orchids grown in the home are epiphytes, meaning they live in nature by clinging to trees or even stones. The roots of these plants are highly specialized organs that differ dramatically from normal plant roots. Of course, it's hard to generalize about anything when it comes to orchids. This is the single largest group of plants in the world, so for every rule, there are 100 exceptions.
Once you develop more than a passing interest in orchids, you will quickly notice how diverse this exotic plant family is. Encompassing genera that yield both the vanilla you love to bake with and fragrances you love to wear, each flower has unique characteristics and care requirements. Compare your plants to some of the most commonly cultivated orchids to help you determine what type of orchid you are growing.