I can’t say anything about TestRail, but Azure DevOps = Team Foundation Server Online with extra goodies.
Probably the biggest benefit to Azure DevOps is the integration with All The Things. As long as it’s set up correctly, you can connect your test automation to test cases, your test cases to work items (regardless of the schema you’re using for the project - that affects whether it’s defects, user stories, bugs, or something else), and hook it all to an Azure Devops build/release pipeline.
Manual test cases can be as detailed or broad as you please - I tend to keep mine broad and use the test steps to cover different settings that a test case needs to cover. You can do anything from stepping through your test case using the web tool to just marking it pass/failed when you’re done testing.
There’s also a ton of plug-ins/extensions, many of them free, that you can use - including a plug-in for Firefox and Chrome that allows you to record exploratory sessions and log them to Azure DevOps, associated with the user story/bug/whatever that you need them linked to.
Honestly, there’s so much there it can be overwhelming at first - it took me months to get my first automated test pipeline working. Now I can set one up in a day or so and get emailed the results.