PaymentMethods = a specific credit card, debit card, etc. Payment Method is basically a term of art so ubiquitous that it's user-facing in UIs and has nothing to do with Stripe.

PaymentIntents is definitely a Stripe abstraction, however, but that's one that I like. It's been a while since I used it, but I remember liking that it allowed me to bundle up everything related to the payment, i.e. the amount, the payment method, etc, and pass it around between server, client, and different views in the client, such that you could really build the exact payment flow you want without touching PCI data.

The Stripe abstractions I have always felt are much clunkier are the distinctions between Products/Prices/Subscriptions/SubscriptionSchedules, etc. A lot of "what lives where?" with those; very clunky to work with.