It's What's on the Inside that Counts
So that's the skin-deep difference. Now let's get to the guts, or the "internal" differences between padfolios and portfolios. Portfolios are typically larger or thicker because they're designed to hold a multitude of items (remember, some are big enough to carry around artwork). Many of them open accordion-style to accommodate more than just papers (although they won't actually make music, unfortunately). On one side of the portfolio there is space for a steno or a legal pad, and on the other side there are extra pockets used to store miscellaneous office items.
A padfolio is kind of like the portfolio's younger sibling. Padfolios are thinner and more lightweight because they are designed to contain "flat" items like paper or notebooks. They have the same space on one side for a notepad or a legal pad, but instead of having extra pockets like portfolios, they usually have only one pocket. This pocket is large enough to store a thin file or several extra sheets of paper. However, there are some versions that have small storage compartments for pens or pencils.