You could think of many different kinds of RP that way, really. The kind of RP you've seen must mostly have been spontaneous RP; the kind of RP where you simply stand around in a cantina or some other place to meet with people and just chat away with them - much like you would in real life. On the other hand, you could have organised RP as well, which means going out there in some attempt to reach a certain objective in character. It largely depends on the organizer whether or not that event ends up having a pre-planned outcome or is completely subject to the decisions made by those involved (I personally prefer the latter). It's easy enough to just RP during missions or even flashpoints if you manage to find someone who you know would be interested in doing so alongside it. I wouldn't recommend assuming every single person you randomly group up with would be interested, as not all of them might automatically be RPers, of course.

Hello fellow former DBer! During my short time in SWTor myself, I've found RP to be largely the same so far, with the exception of the game's engine of course (the lack of chat bubbles in particular is something I had to get used to at first). It was a bit difficult getting into the vibe and the community at first, but rolling along with a guild seems to be one of the safest and easiest means to find yourself a decent share of RP out here (if you haven't already, since I notice now that this response comes somewhat late in regards to the date of your original post). I did find some people RPing out in the open world here and there, but it's always a bit of a question of whether or not to interrupt, since it's mostly been personal RP so far. The most RP you'll find by far, from what I've noticed, is out on the homeworlds like Tython. If you have any more questions, happen to be looking for some RP out there or even need a potential familiar face back from DB, feel free to give me a poke sometime. You'll find my character by the same name as the one displayed here anyway. Enjoy your stay!

I realize my vote would hardly make a difference, but I'd just like to voice my support for this thread. Ever since I started playing as of late, I've immensely enjoyed this game and decided to cancel my subscription on another MMO in its stead. Now, the only thing I truly find lacking are the chat bubbles, which would make life a lot easier, especially if one were to be in an RP-situation.