cargo new my-library
This creates a new directory called my-library containing the cargo config file and a source directory containing a single Rust source file:
my-library/Cargo.toml
my-library/src/lib.rs
These two files will already contain the basic skeleton of a library, such that you can do a cargo test (from within my-library directory) right away to verify if everything works.
cargo new my-binary --bin
This creates a new directory called my-binary with a similar structure as a library:
my-binary/Cargo.toml
my-binary/src/main.rs
This time, cargo will have set up a simple Hello World binary which we can run right away with cargo run.
You can also create the new project in the current directory with the init sub-command:
cargo init --bin
Just like above, remove the --bin flag to create a new library project. The name of the current folder is used as crate name automatically.