The Wikipedia description of "Design language" is actually pretty good. From that article:
A design language or design vocabulary is an overarching scheme or style that guides the design of a complement of products or architectural settings. Designers wishing to give their suite of products a unique but consistent look and feel define a design language for it, which can describe choices for design aspects such as materials, colour schemes, shapes, patterns, textures, or layouts. They then follow the scheme in the design of each object in the suite.
Usually, design languages are not rigorously defined; the designer basically makes one thing in a similar manner as another. In other cases, they are followed strictly, so that the products gain a strong thematic quality. For example, although there is a great variety of unusual chess set designs, the pieces within a set are usually thematically consistent.
As read above, a design language is simply making sure that designs look similar to each other to give off a singular look and feel for a product or company. Styleguides can be used in part to help enforce the design language. Animation and interaction are part of the styleguide as well in the cases you mention.
The only real difference between design language and styleguide is that a design language is a unified feeling and a styleguide is how to accomplish that feeling.