Can customers pay with Apple Pay or Google Pay on my ordering website?

Often yes, through Stripe. Apple Pay works on Stripe's hosted Checkout with no extra setup. Google Pay is switched on in payment settings, but not for Stripe accounts based in India.

• Apple Pay: Stripe accounts worldwide can accept it. On hosted Checkout it needs no additional setup.
• Google Pay: Stripe accounts worldwide except India can accept it. Turn it on in payment methods settings; your page must use HTTPS.
• Stripe shows a wallet only when the customer's device and browser support it.
• Wallets are a Stripe feature, so what customers see depends on your payment provider.