uvx ruff check and uv tool install ruff do different things. uvx, an alias for uv tool run, resolves the tool into a cached ephemeral environment and runs it; nothing is added to your PATH and the environment can be discarded. uv tool install creates a persistent per-tool environment and links executables into the tool bin directory, which is what you want for something you invoke daily.
The gotcha is that neither one installs into your project venv, so a tool run this way cannot import your project's code. Plugins are the usual casualty: uvx mypy will not see a type stub package you added to the project. Pull them in explicitly with --with, as in uvx --with pandas-stubs mypy, or install the tool with uv tool install mypy --with pandas-stubs.
When the command name differs from the package name, uvx --from httpie http disambiguates. Make sure the bin directory is on PATH by running uv tool update-shell once, otherwise installs appear to succeed and the command is still not found.