Is the epidural for this procedure (BA, TT, BBL, liposuction) the same or is it different than the one used for labour?

An epidural is a type of nerve block. Yes it is the same one that is used during childbirth. For the procedures you are considering I recommend general anesthesia. This is for your safety, your comfort during the procedure, as well as giving your surgeon the opportunity to maximize your results.

Thank you for the question.
There are many different types of acceptable techniques of anesthesia that can be used for the breast augmentation procedure. As long as the plastic surgeon and anesthesiologist involved are “expert” at the technique selected, patients generally do very well.
My advice to patients is: concentrate on choosing your plastic surgeon carefully.  Concentrate on appropriate training, certification, and the ability of the plastic surgeon to achieve the results you are looking for. ***Ask to see lots of examples of his/her work.
Once you have chosen your plastic surgeon carefully, everything else, including the type of anesthesia ( and most importantly SAFETY concerns)  will follow. 
Having said that, in my practice I prefer the use of general  anesthesia provided by a well experienced board-certified anesthesiologist. I find the use of this type of anesthesia provides for a safe, comfortable, and immobile patient;  these conditions are important when it comes to achieving optimal outcomes.
 
Most patients describe the experience of anesthesia as a "pleasant nap";  assuming you are working with a well experienced plastic surgeon and anesthesiologist, your "wake up" should be smooth, as well as pain and anxiety free. There are a variety of methods available to help with pain control.   
Best wishes for an outcome that you will be very pleased with.

The epidural is the same, but the experience is different. When you were pregnant, it was not safe to sedate you before the epidural went in. This time, you don't have to worry about that! In our office, you are "drunk" before the catheter goes in, so you won't remember it. Now, as for your labor epidural not working. That you need to discuss with you surgeon and their anesthesia staff. Sometimes during a c section, you feel a lot of pressure and tugging. That's normal. Did you feel anything sharp? The epidural for your tummy will include sedation so you will sleep through the procedure and not feel that. Also, most offices would be able to switch to a different type of anesthetic if necessary in case the epidural "doesn't take."  I am a big fan of epidurals for tummy tucks -- less postop pain, faster recovery, lower DVT risk. You'll do great. Good luck!