People use "gateway" and "processor" as if they're the same thing. They're partners, not twins.
The gateway
The gateway is the digital doorway. It securely captures the card details at checkout and encrypts them for transit - think of it as the card reader for the online world.
The processor
The processor takes it from there, shuttling the transaction between the card networks and the banks to get it authorized and settled.
Why it matters to you
Card-present businesses often only need a processor; online businesses need both. Knowing which is which helps you avoid paying for tools you don't use.