Passion can be seen as desire, emotion and intensity. Compassion can be expressed as care, empathy and charity. They at times can be closely related to each other and can be expressed at the same time. However, when you consider them as individual possibilities in how you interact with others, you can clearly see their differences in action.
The Internal vs. External
The differences between passion and compassion can first be conceptualized as internal and external. Passion can be seen as beginning with an internal feeling that manifests itself externally as a expression of emotion. Compassion on the other hand can be seen as something that you extend and give as an act to another person. It is the external manifestation of a multitude of emotions which can be argued to include passion.
One Without The Other
It is said that passion and compassion tend to drive each other. However, they are often independent. Passion can be the beginning of caring intensively about something or someone and that can lead you to show compassion, but not always. For example in the business world, passion for your job is encouraged but compassion is often forgotten. To have both in the business world suggests that your job is not being done fully because you are giving some of your intensity and drive away by practicing compassion.
Level of Intensity
When you think of compassion you think of someone caring for a cause or an individual. This is not passion. Compassion may cause you to care but it may not cause you to act on that at an intensified level. An example would be a person who sees the homeless and feels sorrow and compassion for their situation. They may act on this by donating money. A person who is passionate about the homeless may not even think about how to help but they may be very emotional and passionately speak out on it.
Consistancy of Commitment
When you think of passion you can see it as something driving a person over and through multiple experiences. Passion in this way takes time to fade. A passionate person is committed to someone or something in a manner that drives them to express this situation over time. In the example above a person passionate about the homeless may speak out on this any time that it comes up or may seek out chances to express their feelings. On the other hand the person who felt compassion may never donate again. Their feelings of compassion could then be addressed in one moment never to be revisited.