It's like Twine.
AFAIK Twine is mostly for publishing directly to the web.
Ink is more suited for embedding in a game which adds additional presentation or gameplay stuff on top of the text, using some other language/engine (like Unity). It will handle the text stuff, and provide hooks/bindings for the rest of the game to use.
I think the presentation is different. In Twine you have multiple pages of text, linking and branching using hyperlinks. You can publish your game as a html file.
Whereas, in Ink, IIRC the flow is like scrolling text. New passages appear below the older ones, depending on choices made. I don't know a lot about Ink to be honest.
It is similar to twine. The Inkle games so far have either been adaptations of Choose Your Own Adventure-style books or very much like that. You read some text and then you have a few choices. They also have some very basic combat in the Sorcery! adaptations.