It really depends on the details of the license, and what is being licensed. If you are talking about development software, then a personal use license is usually good for anything you create for yourself and yourself only (not for your partnership or even for "You, Incorporated"), whether the site makes money or not. You would not be allowed to use the software to create anything for anybody else, so advertising yourself online as a web developer while holding a "personal use" license for the software you use might not be a good idea.
If you are talking about images, fonts or other media, then a "personal use" license would strictly forbid any commercial gain. It's not the designer/developer that matters in that case, it's the context in which the media are used. You can usually use the media on a site that you have developed for somebody else, provided that there are no explicit restrictions stating otherwise. In this case, the "use" is the web impression, so if the web page the media appears on is non-commercial, and you have explicitly omitted the images used from any design/development contract, you may be able to include the media in a design you've done for a client (but it's always best to check with the artist or copyright holder if you can, as a courtesy if for nothing else).