External wiki
External or public wikis are wikis that are freely accessible on the Internet. They serve as resource centers or hubs for knowledge on different topics. Notable examples are Wikipedia and WikiTravel (both using MediaWiki open-source wiki software).
Internal wiki
Internal, or private, wikis are limited to a certain team within a company and sometimes to entire enterprises. They are used for managing internal knowledge base for a company. Organizations and enterprises often maintain their processes, procedures, guidelines, and policies in private wikis.
Personal wiki
Personal wiki differs from public and private wikis by their scope and intended audience. In many cases they also differ technically. In comparison to the standard wiki, personal wiki has a single owner and user - you. They contain information that is of your personal interest and, normally, they are not intended to be publicly accessible.
This changes the technical requirements to the wiki engine for personal wikis - you no longer need a public web server and in some cases any server at all! In these cases it is best to use desktop wiki software that works as standalone local and offline wiki software.
So a personal wiki is always a single user wiki. When it is installed on your own computer it is also a desktop wiki and a local wiki. And in most cases it is also an offline wiki since the data resides on your computer system and you need no Internet connection in order to access it. Some apps can be installed on a thumb drive or an USB stick. In that case you have a portable wiki software.