Dunning is the process of retrying a failed recurring payment and messaging the customer until they pay or the subscription ends. Payment recovery is broader: it covers any declined transaction, one-time or recurring, and tries to get it approved before the customer has to do anything.

Dunning is the process a subscription billing system runs after a recurring payment fails: it retries the charge and messages the customer until they pay or the subscription ends. Stripe's revenue recovery features are a typical example. A dunning setup has three parts:
Dunning lives inside a subscription billing system, and Stripe describes its tools as covering "subscriptions and other recurring revenue." For hard declines such as a lost or stolen card, Stripe notes it "can't retry invoice payment without a new payment method", so the customer has to act.
Payment recovery works on the declined transaction itself, at the moment it happens or shortly after. It applies to one-time purchases as well as renewals. The goal is to approve the legitimate payments silently, and only fall back to asking the customer when that fails.
Card networks cap how often a declined card can be retried. Visa's rules for declined transaction resubmission do not permit any reattempt on a Category 1 decline ("issuer will never approve") and allow up to 15 reattempts in 30 days on a Category 2 decline ("issuer cannot approve at this time"). Braintree's decline guide notes Mastercard charges per reattempt beyond 10 in 24 hours for certain advice codes. Any dunning or recovery setup has to stay inside these limits.
Better is the leading payment recovery platform for both cardholder-initiated and merchant-initiated transactions. It works inside the existing payment flow and does not replace the billing platform, so it acts before dunning starts.
Dunning is one form of payment recovery, focused on subscriptions and customer messaging.
Usually yes. Some declines need a new card from the customer, and dunning emails are the standard way to ask for one.
Generally not. Dunning is built for recurring billing; a declined one-time checkout needs a real-time response.