The therapists I currently have for my kids see me right along with the kids. Essentially family therapy. If the kids want alone time with the therapist I get kicked out. This has happened only once so far, for DD1's first official session. She wasn't uttering a word with me in the room.
So far, there is nothing new getting discussed in therapy. IOW the therapist isn't saying or teaching any skill that I haven't already said or taught to the kids. that doesn't mean it's wasted time. Son and DD2 are getting info from an outside source and learning that mom is NOT crazy and what she's been telling them all along is good information. DD1, on the other hand, is being resistant to Therapist just as she is resistant to me. So I'm still waiting for something "new" to come out of this.
I do not currently have my OWN therapy, but if I decide to go, I will most certainly go see someone different. If I need help with MY issues, I don't want them confused with "family" issues. For example, if one day I REALLY can't stand to be around my kids, that is MY issue, and not a reflection of how I parent them when I'm feeling that way. While most therapists try to remain objective, they are human, and it's too easy to muddle everyone's problems together. For that reason, I also wouldn't feel comfortable divulging my dark ugly secrets to the same person seeing my kids and therefore would not get real benefit from seeing the same person.
So to answer your question, it's both. See your kids' therapist regarding kid issues - parenting techniques, 'handling' your child, etc. Get your own therapist for YOUR issues that you wouldn't reveal in front of your child.