From my perspective, the audience is somewhat different. This is particularly true when the designer is younger with less experience as would be the case for students looking for internships or recent grads looking for their first full-time job. (Which, by the way, is what my original post is about: entry-level students and their first professional portfolios.)
If you’re looking to get hired as an in-house designer by a design manager, you’re presenting your skills, thinking and workflow in the hopes that employer will see you as an asset to their team. They will see the skills and talent and hopefully recognize the potential that young designer has and the contribution they could make to their organization. As a design manager, they’ve probably seen their fair share of portfolios and they know what they’re looking at and what they’re looking for.
It’s similar with finding clients except that in many cases those clients may not be designers themselves. As such, they may not understand what they’re looking for in the same way a design manager looking to hire an in-house designer would. Plus, they are more typically looking for a designer to work with them on a specific product and they’re trying to assess skills, experience and capabilities. The value proposition, resulting relationship and expectations are different.
I’d also add that whereas a student or recent grad might include their CV/resume within their portfolio, making it clear what experience they have/don’t have, but this seems to be less the case on a website. I regularly caution my students that if they plan to do freelance or contract work, they should be very honest and straightforward with regards to their level or expertise. Misleading a client (even via omission) can lead to a misalignment of expectations and a bad experience for both parties.
Of course, later in a designer’s career, these two intended purposes could be served by a single website. But the level of experience and expectations are different.