I had a couple of questions about this, so I looked up the answers. Figured this might be helpful for others.

Is there anything that distinguishes this from a lookup table? Or is it just two ways of doing the same thing?

A lookup table will populate the return values for all possible returns when creating the array. This is fine if you're just creating a few hard-coded strings, as in Jeffrey's example. But in general, match is the better option, especially if you're hitting the database.

$status = match($request_method) {
    'post' => $this->handlePost(),
    'get' =>  $this->handleGet(),
    'head' =>  $this->handleGet(),
};

match also allows for multiple lookups to return the same value.

$status = match($request_method) {
    'post' => $this->handlePost(),
    'get', 'head' =>  $this->handleGet(),
};

What about switch's default case? How is that handled in match?

It's exactly the same. Just use the default keyword.

$status = match($request_method) {
    'post' => $this->handlePost(),
    'get', 'head' =>  $this->handleGet(),
    default => throw new \Exception('Unsupported'),
};

Match Expressions