Like Lightroom, darktable handles collections of images and allows applying a recipe of alterations to tune up each image. But it is like Photoshop in that it allows a great deal of volition in what happens to the image. This is especially true in darkatable v3, which allows re-ordering of of the various algorithms (also known as the pixel pipe) which work on an image.
Unlike Photoshop, which is primarily a pixel-based editor, both Lightroom and darktable tend to work on the image in aggregate, with tools which are particularly useful to images created via a lens and digital sensor. Lightroom has a lot of its choice/sequence of tools "pre-baked", and there's a lot of wisdom in its choices.
The tools in darktable are more esoteric. They're based on a variety of traditional and recent mathematical work in image processing. It takes a bit more knowledge and taste to choose the best tools, and set their parameters well for a particular image.
Depending on hardware, you may find that the Adobe tools are a bit faster.
As a sibling poster mentions, of course darktable is open source, and not subscription-based. It has an active development community. As Pascal Obry, who managed the current release, writes in an email to the darktable list: "It is also an important release as new developers have shined in and proposed some amazing features." There's also active community of darktable users who help each other to understand how to use it to work on a variety of images. I find these discussions enlightening in order to gain a more general sense of ways to think about image processing. One home of this community is https://discuss.pixls.us/c/software/darktable.
I haven't used darktable in the last few releases, but when I did, bad hotkeys on MacOS was a noticeable irritant. At the time it felt like many open source tools: powerful but difficult. It might differ today, and the lack of mandatory subscriptions makes it very appealing.
Very abstractly, LR provides more useful specific tools, whereas DT provides more advanced generic tools that can accomplish many different tasks.
E.g. the equaliser in DT can be used for denoising both chroma and luma, and dynamic range, and many other things. The LAB color curves are super powerful for all sorts of colour correction. Parametric masks allow powerful local-ish editing.
