If you sign up for Card Ladder through the website you'll have payments processed by Stripe. They are the industry leader in this field and you can learn more about them here.
If you sign up for Card Ladder through your App Store app on your iPhone then your payments will be processed through subscriptions managed by Apple. You can learn more here.
If you sign up for Card Ladder through your Play Store app on your Google Device then your payments will be processed through subscriptions managed by Google. You can learn more here.