Vortex is a file format. In their canonicalized, uncompressed form, vortex files are simply Apache Arrow IPC files with some of the bits and bobs moved around a bit (enabling transformation to/from Arrow), plus some extra metadata about types, summary statistics, data layout, etc.
The Vortex spec supports fancy strategies for compressing columns, the ability to store summary statistics alongside data, and the ability to specify special compute operations for particular data columns. Vortex also specifies the schema of the data as metadata, separately from the physical layout of the data on disk. All Arrow arrays can be converted zero-copy into Vortex arrays, but not vice-versa.
Vortex also supports extensions in the form of new encodings and compression strategies. The idea here is that, as new ways of encoding data appear, they can be supported by Vortex without creating a whole new file format.
Vortex-serde is a serde library for Vortex files. In addition to classic serialization/deserialization, it supports giving applications access to all those fancy compute and summary statistics features I mentioned above.
You say "Vortex is a toolkit for working with compressed Apache Arrow arrays in-memory, on-disk, and over-the-wire," but that's kind of like saying "MKV is a toolkit for working with compressed AVI and WAV files." It sounds like Vortex is a flexible file spec that lets you:
1. Work with Arrow arrays on disk with options for compression.
2. Create files that model data that can't be modeled in Arrow due to Arrow's hard coupling between encoding and logical typing.
3. Utilize a bunch of funky and innovative new features not available in existing data file formats and probably only really interesting to people who are nerds about this (laypeople will be interested in the performance improvements, though).