DBT is part of CBT. So not really different systems.
No, they are different. They only share in common the concept that how we think is related to how we feel and act.
Marsha Linehan, who conceived of DBT, did so after realizing the CBT was ineffective as a treatment protocol for people with Borderline because it did not sufficiently address the need for acceptance of the disorder, as well as the distress tolerance skills that are essential for day-to-day living while improving. CBT also does not address the specific kinds of relational dysfunctions people with BPD have.
It can be much easier to understand DBT if you've first done a
bit of CBT - just for understanding the concept of cognitive therapy, generally.
For borderline personality disorder, DBT is the absolute first-line therapy. And for people with BPD diagnosed, or even with simply very prominent BPD traits - doing the classic protocol for DBT is really not a bad idea. It has a lot of support and education built in.
But there are also more streamlined ways to learn the techniques. I strongly recommend finding a DBT group where you'll be guided through them. You can take yourself through the books, but honestly - you'll struggle less if you can get into some kind of structured program where you can learn the basics.
Many hospital outpatient programs use DBT techniques, as well as there being specific groups dedicated to running DBT workshops and seminars.