I'm Miles from the Social Care team at Shopify. I can totally understand the confusion here. The great thing about accelerated checkouts is that they require less work from the customer by being able to tap into their pre-saved information on Shop Pay, Apple Pay, Google Pay and PayPal Express. It avoids them needing to type out all their details.
When a customer clicks an accelerated checkout option, it will take them to their pre-saved details, but will also show them the same shipping options as a customer who goes through the manual checkout. Customers will not receive free shipping through these options - unless free shipping is already an option on your page. I recommend checking out our guide on accelerated checkouts to learn more about how they work.
If your customers are incorrectly receiving free shipping after using these options, please let me know. If you could also link your website, I'll be happy to test it out so I can replicate the issue. This is also something I recommend you try. Complete a test checkout using one of the accelerated options so you can view the flow and make sure it's displaying the correct shipping. Also, double check your shipping settings (Settings > Shipping) to make sure everything is set up correctly there. You can learn more about setting up shipping right here: https://bit.ly/3eNUUll.
Please let me know if you require any other assistance with this at all.
Apologies for the delay in getting back to you. I've just tried accessing your site to test it, but it appears that none of your products has an Add to Cart button. Is this intentional? If not, I would recommend checking your settings to make sure you have the checkout enabled on your account (Settings > Checkout). If you're having issues, please let me know.
For Apple Pay to appear, you need to be using a device that's registered for Apple Pay (iPhone, Mac etc) and have it set up with a payment card. I did try to test this but as there was no Add to Cart options, I was not able to try it for you.
To see the Apple Pay button, your customers must use Safari on iOS 12.1 or macOS 10.14.1 on one of the following devices:
You can learn more about the Apple Pay process here: https://bit.ly/38tmvsf.
To see the Google Pay button, your customers need to be using one of the following supported browsers on desktop or mobile:
They also need to be registered to use Google Pay in order for the transaction to work as intended. If you're seeing an "unexpected developer error" make sure Shopify Payments is not set to test mode (Settings > Payments > Manage).
Check out our guide on enabling Google Pay for more information.
If you're continuing to see issues, please let me know.