Each class you walk into will be different, so it's tough to pinpoint specific distinctions, but this is one of the most frequently asked questions.
Many yoga classes are flexible in routine. Postures, sequences and variations can be combined into tens of thousands of routines to create a class. So it will be up to the style of yoga you practice and the teacher guiding you to decide what's on the agenda. There are some styles of yoga that have more of a set plan, such as Ashtanga and Bikram.
Pilates classes are a little more structured. Because of this, you will more likely know what to expect when you walk into the door of a Pilates class than in a yoga class.
Another element that is often (but not always) brought into a yoga class is meditation. Many yoga classes use a chant or meditation to bring in the focus and dedication at the beginning, and to seal in and appreciate the benefits of the practice at the end.