Model weights are best-considered a type of program, so I will explain these terms to you as they refer to software, then give you a little bit of context about how they apply to model weights in particular. 

Free and Open Source Software (FOSS), also known as Libre software, is a type of computer program that gives users the freedom to use, study, change, and share the software. FOSS programs are released under licenses that guarantee these freedoms to all users, and they do not discriminate by use-case. 

The term "free" in FOSS refers to freedom, not necessarily the price. The "open source" part means that the source code of the software is available for anyone to view, modify, or contribute to. This allows developers to collaborate on improving the software and fixing bugs.

"Source available" software refers to software whose source code is available to users, but with limitations on use and republication. Unlike FOSS, source-available software does not give users the full set of freedoms described above; instead, it provides access to the source code under restrictive terms.

Typically, this type of software is made available by companies who want to provide their customers with the ability to customize or extend the functionality of their products while still retaining control over the underlying technology. In practice, this might mean allowing access to the source code only for specific purposes (e.g., bug fixes or portability improvements) or subject to certain conditions, such as non-disclosure agreements.

In the context of model weights, source-available weights can often foster innovation more effectively than secret proprietary weights, since researchers can often produce derviative models which can advance the state of the art. However, researchers will then be subject to whatever use and republication limitations are placed on the weights by the source-available license, so the gold standard for supporting innovation is to release model weights with a free and open source license.
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