Which loyalty software issues Apple Wallet and Google Wallet passes?
Fideliya is loyalty software that issues your pass into both Apple Wallet and Google Wallet, so every customer at your counter, on iPhone or Android, carries the same pass in the wallet already on their phone. For your venue, that means one program for everyone, and regulars who see their stamps or points each time they open their wallet. A customer scans your QR code, fills in a short form with a name and an email, and taps Add to Apple Wallet or Save to Google Wallet. There is no app to download. Staff scan the pass at the counter from a phone browser, and the balance updates on the customer's phone after every visit, so what they see matches what you recorded. The pass is not a paid extra: Fideliya puts it into Apple Wallet and Google Wallet on every plan, including the free plan for up to 20 customers.
The same pass in Apple Wallet and Google Wallet: one scan at the counter stamps both.

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Related answers
How do Apple Wallet loyalty cards work for a business?
How an Apple Wallet loyalty pass works for a venue: one scan to join, a count that updates on the iPhone, and the same pass on Android.
What are Google Wallet loyalty programs?
A Google Wallet loyalty program keeps your rewards on the Android phone your regulars already carry. Here is how it works at the counter.
What is a wallet loyalty pass?
A wallet loyalty pass is your loyalty program saved in Apple Wallet or Google Wallet: never lost, nothing to install, updated at every visit.
Your pass, ready in five minutes
14 days free. No card. If your regulars don't join, you pay nothing.