Trolley actually uses Checkout in the UI, so we don't compete directly.
What Trolley gives you is - you don't need a server!
If you use Checkout yourself, adding the widget to your front end is really easy - but you also need to provide some code in the backend that processes your form submission and then does the token exchange with Stripe to actually make the charge on the customer's account.
That means you either need to be on some kind of all-in-one e-commerce suite, use WordPress and some plugins (and either host it yourself or pay someone to) or build and run some infrastructure of your own (heroku, DO, EC2, maybe FaaS if that's your thing)
Think of Trolley as a Stripe backend-as-a-service with a useful UI feature :-)
Trolley requires and uses Stripe Checkout, but it's there to make it easier and faster to sell - especially if you want a static HTML site - than checkout alone.