Paolo Soleri received his training from Frank Lloyd Wright who was consider a pioneer in what is term Organic Architecture.
While there are associations with Organic Architecture and Soleri's design aesthetic, he recently in a discussion with Chinese professionals visiting Arcosanti sought to distance himself from an association with the Organic Architecture Movement.
His criticism of the term was that architecture is a human endeavor and thus cannot be associated with natural systems to call it organic is in his mind absurd.
However we can see that the buildings he designed particularly at Cosanti did take into consideration both natural elements and forms in the design of the buildings and also in molding transitional forms between the built environment and the natural surroundings. Silt casting which Soleri takes a lot of pride in developing is the use of a natural material - silt - which is used to give concrete a more natural feel and texture.
A more careful parsing of the word phase Organic Architecture is to see it was coined to reference a union or reunification of the human reality with an understanding of natural systems and processes in the design of architecture. An example is seeing natural forms and being inspired by those forms enough to create designs that carry that inspiration into the built environment and the architectural space.
There are many terms in the design, engineering and architecture fields that convey similar things. These include Ecological Design, Ecological Architecture, Green Architecture and Eco-Building. To try to reconcile these terms is important so that people don't get confused.
Green Architecture is the application of green technologies and approaches to the field architecture
Ecological or Green Design is the wide ranger principles of deeper ecological understandings into the designing/making of products including buildings
Ecological Architecture - is similar to Ecological Design but more specific to Architecture
Green or EcoBuilding refers to the construction of buildings and built environments using more enlightened principles of building with consideration of nature and natural systems
In contrast to the above definitions Organic Architecture in my definition and looking at Wright's origins is more focused on the design of the building inspired by nature and its surroundings rather than a holistic process that considers the ecological impact of the building process and operation of the building itself.
References:
Wikipedia post on Organic Architecture: http://en.wikipedia.org/wiki/Organic_architecture