What is the Rust equivalent to a try-catch statement?

There is no try catch statement in Rust. The closest approach is the ? operator.

However, you do not have to create a function and a match statement to resolve it in the end. You can define a closure in your scope and use ? operator inside the closure. Then throws are held in the closure return value and you can catch this wherever you want like following:

fn main() {
    let do_steps = || -> Result<(), MyError> {
        do_step_1()?;
        do_step_2()?;
        do_step_3()?;
        Ok(())
    };

    if let Err(_err) = do_steps() {
        println!("Failed to perform necessary steps");
    }
}

Playground

Is it possible to handle multiple different errors at once instead of individually in Rust without using additional functions?

There is a anyhow crate for the error management in Rust mostly recommended nowadays.

As an alternative, There is a failure crate for the error management in Rust. Using Failure, you can chain, convert, concatenate the errors. After converting the error types to one common type, you can catch (handle) it easily.