SSNs are also called attack submarines.

SSBNs are the big guys who carry large quantity of nuclear warhead ballistic missiles whose job is to lay low, stay hidden to maintain a first/second strike capability.

SSNs are the small guys who are fast and agile out on a hunt for enemy submarines. They also have limited capacity to launch cruise missiles on naval and land targets. Also known as the “fast attack subs”.

The Soviets/Russians also have SSGNs which are in between the two and capable of carrying long range guided cruise missiles, whose job is to stay hidden and then launch a large salvo of cruise missiles capable of overwhelming the enemy fleet’s defense.

Then you have the SSKs - the really small guys, the diesel-electric attack subs that operate on batteries and are extremely quiet but have limited range. They are usually built for littoral (coastal) defense rather than blue water naval power projection.