Does cargo install have an equivalent update command?

There is no such command in vanilla cargo (well, there's cargo install but that's for dependencies), but since cargo supports third-party subcommands there is an answer: the cargo-update crate.

Install as usual with cargo install cargo-update, then use cargo install-update -a to update all installed packages, for more usage information and examples see the cargo install-update manpage.

_{Disclaimer: am author}

A solution I've found is to add the --force flag to the install command. For example cargo install --force clippy. This will effectively re-install the latest version.

As of Rust 1.41.0, you can use the following command to update crates to their latest version:

cargo install <crate>

This came from pull request #6798 (Add install-upgrade) and was stabilized in #7560 (Stabilize install-upgrade).

How does it work?

Instead of failing when cargo install detects a package is already installed, it will upgrade if the versions don't match, or do nothing (exit 0) if it is considered "up-to-date".

Forcing an upgrade / re-installation

The following command will always uninstall, download and compile the latest version of the crate - even if there's no newer version available. Under normal circumstances the install-upgrade feature should be preferred as it does save time and bandwidth if there's no new version of the crate.

cargo install --force <crate>

Documentation

Further information can be found in the GitHub issue rust-lang/cargo#6797 and in the official documentation chapter.