Disa is a genus of beautiful plants with rather triangular flowers, often red. They require VERY different care than other types of orchids, so it's easy to kill them if you don't know what you're doing. In particular, they like it wet and should never dry out. The best-known Disa is Disa uniflora, which in South Africa is known as the Pride of Table Mountain.
The Lycaste orchid genus, similarly to its relative Anguloa, likes intermediate-to-bright light, intermediate-to-cool temperatures, and high humidity. The flowers look rather different, though; they are more-or-less triangular in shape because the sepals point outward while the petals point forward. These orchids are very fun to grow, and will thrive if you get their care right.
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.
This is not a type of orchid you’ll want to place on your windowsill, because the stems grow up to four feet high. Phaius orchids have large, strappy leaves, and they usually produce petals that are yellow, purple, or white. Also known as the Nun’s Cap orchid, it is a winter bloomer and makes a great addition to anyone’s garden, regardless of what else is planted there.
Oncidium, perhaps more accurately the oncidium alliance, are a group of plants from South America that span a wide range of habitats. Inside the oncidium alliance there are a number of genera that hybridize freely to create what we call intergeneric oncidium hybrids. These can come in all sorts of shapes and sizes but are generally characterized by large quantities of small to medium flowers borne on a branched stem that generally forms a Christmas-tree shape. The most commonly identified Oncidium are the yellow “dancing lady” type.
Here again, the type of potting mixture will be a major factor in determining how often you should water your orchid. You should also pay attention to the condition of the potting mixture, as aged growing medium that has broken down into finer particles will hold more water and take longer to drain than fresh medium, thus requiring less frequent watering.