In addition to being different in size, padfolio and portfolio are different in function. Padfolios are slim and lightweight which is designed to hold just some paper on one side and minimal contents (like a few notes or a file and a couple of pens) on the other.
Portfolios on the other hand, are designed to hold more items, so they include more pockets and organizational details -- some even open accordion-style. Normally, even a smaller portfolio will easily accommodate a laptop, multiple files, a calculator, and other accessories. If it is a large portfolio, it can include more items.
The most important factor in your padfolio vs. portfolio decision is how you’ll be using it. If you need something simple to bring to a lunch meeting or interview, go for a classic leather padfolio. Need something to carry at that three-day conference? A nice portfolio may suit you better.