A payment processor is the service that takes card payments for event registrations and moves the money to the organiser's account.
The processor moves the money. A gateway passes card details to it. The event platform sits in front of both and decides which it can connect to. Conflating the three is why "does it support Stripe" gets different answers from different vendors.
The question that matters for cash flow is whose account registration revenue lands in and how quickly. Processing through your own merchant account means funds arrive on the processor's schedule. Processing through a platform's account means waiting for the platform to pay out, which can be after the event has happened.
Card processing fees are charged by the processor, not by the event platform. Organisers decide whether to absorb them or pass them to ticket buyers at checkout, and that decision belongs in the pricing model before tickets go on sale.
Stripe and Square are available globally. Braintree, Authorize.net, NMI, CyberSource and TouchNet depend on plan tier, and Payflow Pro is White Label only. Accelevents does not take a percentage of card processing fees. See ticketing and registration.