How would my code identify between /quotes/:id and /quotes/random?

Based on your own comment, you could check if the :id (req.params.id) is a number by trying to coerce it to a number. If it is not, then you could call next(); to pass on to the next middleware and eventually return a 404 error.

router.get('/quotes/:id', (req, res, next) => { if (isNaN(parseInt(req.params.id))) { next(); } else { //perform response stuff here } });

The if statement parses the id as a number, if it fails it will return NaN (not a number) which is caught by isNaN() and returns true if the id is not a number.

I think the answer to your original question is quite simple. You made a mistake in your route. The random route is supposed to be /api/quotes/quote/random.
I was wondering how the /quotes/:id route didn't get mixed up with the /quotes/quote/random route when it seems that /quote/random would fill in as the :id in the first route.
It seems that if there is a "/" within the id and it isn't expected, the router simply moves on to the next middleware.
Try testing out a get request to /api/quotes/quoterandom or /api/quotes/quote and you will see a 404 error if you have a try...catch block set up to catch an empty quote object. Then if you make it /api/quotes/quote/random it will work.

I just realized I misunderstood Akshay, so let's handle what they're talking about: making sure a "/quotes/random" request does not get resolved by "/quotes/:id". For this, we just need a simple conditional:

router.get(
  '/quotes/:id',
  asyncHandler(async (req, res) => {
    const { id } = req.params
    if(id === "random") res.redirect('/quotes/random')
    const quote = await records.getQuote(id)
    if (quote) return res.json(quote)
    throw new Error("Could not find quote")
  })
)

And that's all! But honestly, I would just put "/quotes/random" before "/quotes/:id" if you don't want to change the path to "/quotes/quote/random". A request sent to a node server checks the first router listed to the last. We as developers should use that functionality to our advantage. It's not a bug, it's just how it natively works and it allows us to set up proper gateways for our routes. So just pop that "/quotes/random" to the top of your routes.js (or at least above "/quotes/:id") and your problems are solved!

If I am understanding what you're asking is you want if someone passes in a bad req to automatically generate a random quote? Meaning you want to change:

localhost:3000/api/quotes/dfdfsdfsd

instead of getting a message: 'Quote not found.' you want some random post returned? To do this you can leave /quotes/quote/random and just modify the code for '/quotes/:id'. Instead of returning an error you can always return something:

router.get(
  '/quotes/:id',
  asyncHandler(async (req, res) => {
    let quote

    quote = await records.getQuote(req.params.id)
    if (quote) return res.json(quote)

    quote = await records.getRandomQuote()
    return res.json(quote)
  }),
)

codingchewie's answer isn't a bad one, but it is repeated code and infringes on the territory of another route we created. I would suggest adding a redirect like this for the use case they presented.

router.get(
  '/quotes/:id',
  asyncHandler(async (req, res) => {
    const quote = await records.getQuote(req.params.id)
    if (quote) return res.json(quote)
    res.redirect('/quotes/random')
  })
)

Coming from a lot of years writing routes in the Laravel PHP framework, I have always gone with putting all routes with a direct URL above those that expect a parameter. It's easier to read and flows without having to check if a parameter is present or if it matches a type or specific value.

Express routing works the same way. In my solution, the router will first run /quotes/random because it is explicitly defined. Otherwise, it will skip to the next route with a parameter.

// GET request to return a random quote
router.get('/quotes/random', asyncHandler(async (req, res) => {
    const randomQuote = await records.getRandomQuote();
    if (randomQuote) {
        res.json(randomQuote);
    } else {
        res.status(404).json({message: "Sorry, there are no quotes"});
    }
}));

// Send a GET request to /quotes/:id to READ a quote
router.get('/quotes/:id', asyncHandler(async (req, res) => {
    const quote = await records.getQuote(req.params.id);
    if (quote) {
        res.json(quote);
    } else {
        res.status(404).json({ message: "Quote not found" });
    }
}));