Your explanation agrees with what most people would say, according to an extensive body of research. (I used to do research on online communication, not specifically on emoticons, but since those tend to crop up in many different kinds of online communication there's a lot of research on it, so I have read quite a bit about the subject.)

As for the "J", that usually means that the sender used a smiley in MS Outlook. The proprietary format used by Microsoft doesn't translate to other email software, so Outlook smileys are translated to a "J".