With the free version, users can expect all the same processing power of DaVinci Resolve Studio, but it will limit project mastering and output to Ultra HD resolutions or lower. Additionally, DaVinci Resolve 17 only supports a single processing GPU on Windows and Linux and two GPUs on the latest Mac Pro. If you need to export 4K, you'll want to consider upgrading to DaVinci Resolve Studio 17.
The paid version has a one-time price tag of $295, and you'll have access to a ton of other tools like motion blur effects, temporal and spatial noise reduction, de-interlacing, HDR tools, camera tracker, multiple Resolve FX, 3D stereoscopic tools, remote rendering, as well as collaboration tools to work remotely with other users.
The latest version is packed with features like an updated Clip Inspector, smart reframing for social media, better live previews, a Color Wrap tool that lets you adjust two color parameters at once, targeted grading with Magic Mask, improved scopes, and a ton of others. You can read more about it here.
When updating to version 17, it requires a database upgrade from DaVinci Resolve 16.2.7 and previous versions. Blackmagic Design strongly recommends that you back up your existing database (both DiskDB and PostgreSQL) before performing an upgrade.
You can download both versions of DaVinci Resolve 17 here.