The SSBN has typically been the underwater based nuclear weapon launching platform. But beginning in the mid 80's this was to change.
The other type of submarines besides the SSBN is the SSN, or the Hunter Killer. This submarines mission was to seek and and destroy enemy SSBN's and assorted ships. They were typically armed with 6-8 21 inch torpedo tubes. But beginning with the second batch of Los Angeles Class SSN's, they were equipped with vertical launching tubes just foward of the conning tower. In these tubes were carried Tomahawk Cruise Missiles. Originally intended as anti-ship missiles, someone soon realized that these weapons could also be used as surface to surface stand-off weapons. Following that, they were to be built to be able to accomadate nuclear warheads.
This now gave the SSN's nulcear capapbility, as long as they were fitted with the nuclear tomahawks.