Full trisomy 15 (or you'll see just trisomy 15) is when all of the baby's cells have the extra copy of trisomy 15. In most cases, this tends to be a lethal condition.
Partial trisomy 15 is when only some of the baby's cells have the extra copy of chromosome 15. The severity of this condition ranges.
As in the article, Prader-Willi and Angelman Syndrome are not caused by having three copies of chromosome 15. Rather, sometimes babies start out by having three copies of chromosome 15 and then one is randomly removed. This is called a "rescue". Prader-Willi and Angelman Syndrome occur if the two chromosomes left are not one from mom, one from dad. Angelman is when there is two of dad's chromosomes, Prader-Willi when both chromosomes that are left are from mom.
You can detect trisomy 15 prior to birth by undergoing an amniocentesis or CVS. Talk to a genetic counselor if you need more information.