Basically, Adobe Campaign v6 and Adobe Campaign Standard can be considered as two different applications, while they have many common features and are made in a very similar approach. At the moment, they are the most recent versions of Adobe Campaign, and both are integrated to Adobe Marketing Cloud.
Campaign v6 uses a rich client with a Windows(-only) console, which has been developed for about 15 years already. It can be hosted by Adobe or on-premise. Regularly, new builds containing new features are made available. Upgrading to a new build is optional. This version contains more advanced features and can respond to very complex use cases when it comes to data management and personalisation.
Campaign Standard is based on a Web UI and its development started more recently. It is a cloud-only product that is upgraded automatically in a transparent way as new features are added. The interface is designed to provide the best user experience possible. As of today, it covers more simple use cases and teams are working hard to extend the feature set while keeping improving user experience. You can already find most commonly used features from Campaign v6 (email and SMS channels, reports, workflows, audience management, etc.). Note that at the moment AC Standard is only compatible with Debian 7/8 (64bits) and PostgreSQL 9.3 and above.