Yes, they have the same root; however, they are different concepts.
I'll agree with that, compassion insinuates a kind passion, yet passion is neutral in this respect, you can be passionate about many things that are antithetical to compassion.
Though I think that they are linked because they both stem from the same root: NF sentimentality/sensitive.
Very few people tend to be passionate who are not in strong affinity with their feelings (at least they tend to be less passionate than those who are emoitonally sensitive), and hence if those passions are aimed at a right direction:compassion could be the result.
Do you think that they are linked because of the NF emotionality, even though they depict two disparate external phenomena? Yet, I'd still say that they grew out of the same root.
I think they use the passions to give them purpose. I doubt that T is any more purposeful than F. I speculate that this is where the 'F judging function comes in' they use their passions to give direction to the compassion that has been elicited from them.
Seems to me that passion and compassion are inseparable from one another. Passion is the fundament, compassion is the edifice.